Do Psychological Diversity Climate, HRM Practices, and Personality Traits (Big Five) Influence Multicultural Workforce Job Satisfaction and Performance? Current Scenario, Literature Gap, and Future Research Directions

Growing trends of globalization bringing many challenges for organizations including managing performance of multicultural workforce toward achieving the organization’s objectives. Based on past researchers, many factors that influence employee’s performance have been highlighted, but the nature and scope of these factors have been limited to conventional settings. Therefore, the purpose of this article is to develop a comprehensive framework to better understand the role of the psychological diversity climate, human resource management (HRM) practices, and personality traits (Big Five) in job satisfaction and performance of a culturally diverse workforce. The review of past literature was conducted in the development of a conceptual framework. For this purpose, different databases, books, reports, and business magazines were consulted to evaluate current nature of literature related to multicultural workforce job satisfaction and performance. This conceptual article provides theoretical ground and proposes that psychological diversity climate, HRM practices (recruitment and selection, training and development, compensation and performance appraisal), and personality traits (Big Five) positively influence multicultural workforce job satisfaction. Finally, this article explains that culturally diverse workforce job satisfaction predicts job performance. This article suggests that managers and human resource professionals should develop psychological diversity climate among employees, upgrade HRM practices as per diversity needs, and attract individuals with certain personality traits such as agreeableness, emotional stability, and extroversions. Based on past theoretical review, the proposed framework is developed with the aim to address the gap and contribute to the HRM body of knowledge. These variables have never been explained by past researchers in multicultural setting.

Introduction
Due to rapid changes in nature of work and working conditions, managing employee performance has become more difficult. Human resource management (HRM) is playing active role in helping organizations to improve employee performance. Originally, the concept of job performance was perceived as unidimensional construct but with the growing literature, researchers found that job performance is multidimensional construct. In this regard, Borman and Motowidlo (1993) recategorized job performance into task and contextual performance. Task performance as behavior directly involved in the production of goods or goods provide indirect sustenance to organizations in their technical process, according to Van (2000). Borman and Motowidlo (1993) also described contextual performance as enthusiasm and 851578S GOXXX10.1177/2158244019851578SAGE OpenAl Doghan et al.

research-article20192019
1 King Faisal University, Al-Ahsa, Saudi Arabia 2 Prince Sultan University, Riyadh, Saudi Arabia extra effort for own tasks, volunteering for tasks other than his or her own, helping peers, following rules, and endorsing organizational objectives. Previous researchers mentioned contextual performance as an important dimension of individual job performance (Koopmans et al., 2011). Activities that facilitate the social and psychological growth are considered as contextual performance, usually assist others in completing any task or suggest ways of improvement in organizational process.
Managing task and contextual performance has become challenges for human resource (HR) professionals, and several initiatives have been taken to successfully manage employee performance (Bhatti, Alshagawi, Zakariya, & Juhari, 2019). In this regard, researchers have explored many individual and environmental factors that influence employee performance at workplace. In this situation, managing employee's performance becomes even more challenging when organizations deal with diverse workforce. In the 21st century, when world becomes global village, organizations prefer to gain competitive advantage through diverse workforce which is only possible if they improve their diverse workforce job performance. Diversity management can be defined as "voluntary organizational program designed to create greater inclusion of all individuals into informal social networks and formal company programs" (Gilbert, Stead, & Ivancevich, 1999, pp. 8-9).
Rapid changes in demographic trends force organizations in developed countries to introduce HR strategies to cope with these changing trends and manage diverse workforce effectively, but developing countries are still struggling to manage demographic trends. As demographic trends are continuously changing, organizations in developed and developing countries need to permanently adopt diversity management practices. In this regard, researchers also trying to explore different practices and factors that influence diversity management process but unfortunately limited research has been conducted in past on the relationship between diversity management and work group performance. In addition, researchers perceive diversity management as a HR strategy but past research have conflicting findings about diversity outcomes. However, Myung, Jaeyong, and MiYoung (2017) reasoned that conflicting findings of proposed diversity outcomes might be due to poor conceptualization and operationalization of diversity construct. Furthermore, researchers (Madera, Dawson, & Guchait, 2016;Holck, Muhr, & Villeseche, 2016) argued that embracing diversity helps organizations contribute to improved competitive advantage through enhancing diverse workforce job performance. In addition, Monga (2008) also argued that workforce diversity plays a vital role in gaining competitive advantage if managed effectively. Shen, Chanda, D'Netto, and Monga (2009) argued that diversity issues vary from country to country but gender inequality and multiculturalism is the most common diversity issue worldwide, especially in Western countries. Therefore, cross-cultural and multicultural workforce is a common thread for multinational organizations across the globe (Shen et al., 2009). In this regard, Kelli et al. (2015) argued that the fast-growing trend of globalization demands a higher level of interaction among people of diverse background. Focusing on HRM practices alone is not sufficient to manage cultural differences that exist between people of ethnic origins by integrating using common diversity programs (Ainie & Shamsul, 2013). Workplace diversity should be examined from employee's perspective to understand the impact of HRM practices on culturally diverse workforce. Although previous research have evaluated workplace diversity based on the perspective of employee, the scope of the studies were narrowed to concepts of equality or organizational justice (Edgar & Geare, 2005;Hunter, 2003). Therefore, research studies should move toward expanding the scope by investigating how culturally diverse workforce perceive different HRM practices. Furthermore, if organizations want to gain competitive advantage in the global marketplace, they should have high diversity in workforce. Diversity management focuses on developing specific skills, implementing policies which leads to organizational effectiveness and ultimately competitive advantage (D'Netto & Sohal, 1999).

Related Theories
The proposed conceptual model is developed based on three main theories: social exchange theory, social cognitive theory, and trait theory. For example, Homans (1961) defined social exchange theory as an exchange of activities, tangible or intangible, rewarded or costly, between at least two persons. This explains that when organizations follow certain HR practices, employees in exchange show satisfaction or dissatisfaction which further exhibits good or bad performance. Bhatti, Battour, Ismail, and Sundram (2014) argued that when organizations adopt certain practices such as fair performance appraisal system, unbiased recruitment, development opportunities, and so on, employees show satisfactory feelings in return that help them improve their job performance. Similarly, trait theory explains that each individual acts differently in same situation. Allport (1937) explained that an individual reacts and responds differently in different situations in which culture plays an important role. In this regard, Hofstede's culture factors are a great contribution toward trait theory, which explain that different personality traits act differently in different cultures, for example, culture that is more inclined toward individualism might result in a high correlation with extroversion, whereas individuals living in cultures that are accepting of large inequalities in their power structures tend to score somewhat higher on conscientiousness. Therefore, individuals with different personality traits might exhibit different level of job satisfaction based on their personality traits. Finally, social cognitive theory explains that environmental factors (external factors) play an important role to create psychological climate which encourages individuals to respond accordingly. In addition, cognitive process changes the individual behavior. Therefore, cognitive theory explains that when organizations adopt multicultural practices, employees perceive that environment as favorable situation which results in high satisfaction and better performance. The following sections will further explain the relationships of each variable in detail based on the past studies. James, James, and Ashe (1990) define psychological diversity climate as "employee cognitive judgment of his/her work environment that leads to a perception about his or her organization that is significant to the individual" (pp. 16-17). Employees gain these perceptions from organizational policies, procedures, and working environment, but these perceptions on organizational value for diversity can vary from one employee to another. As stated by Myung et al. (2017), organizational diversity policies and procedures play an important role in improving and enhancing diversity climate. Therefore, HR managers should play a more active role in promoting a more inclusive organizational climate, along with handling issues of diversity. In this regard, Mor Barak, Cherin, and Berkman (1998) support this by suggesting that employees' perceptions toward diversity and discrimination policies in the organization have a tendency to create a psychological diversity climate. Madera et al. (2016) argued that previous studies have largely disregarded the study of perceived positive diversity climate and job satisfaction. In addition, McKay, Avery, Liao, and Morries (2011) added that more and more research has started to highlight the outcomes of perceived diversity climate, which includes job satisfaction and higher organizational commitment. Also, it was argued by Hye, Ung, and Young (2015) that there has been an increase in the employees' levels of organizational commitment and job satisfaction when employees perceive that there is a fair use and application of organizational policies and procedures toward all employees regardless of their gender, race, culture, and ethnicity.

Psychological Diversity Climate
It is possible that psychological diversity climate may hold multiple outcomes and therefore, researchers are observed to be struggling in the effort to highlight these outcomes. This is mainly due to the fact that these outcomes would ultimately support organizations in enhancing employee performance, perhaps by fulfilling employee expectations. In this case, it is argued by Greening and Turban (2000) that employees are known to expect their organizations to manage and play a significant role in their development and growth. Also, having a pro-diversity climate gives an important message to employees that their organization is perceived to be unbiased and that it cares for their well-being (McKay et al., 2011). With that, a conclusion can be made that when organizations integrate psychological diversity climate for employees, they tend to feel satisfied with their job. In terms of diversity management, employees tend to gain more job satisfaction when they perceive that their organization encourages diversity and rejects discrimination. Overall, when a diverse workforce perceives that their organization discourages discrimination, encourages diversity, care for their well-being, as well as their growth and development, they would feel more satisfied with the job, which would further leads to improved job performance. Therefore, the above discussion as basis, this article proposes the following: Proposition 1: Psychological diversity climate positively influences multicultural workforce job satisfaction.

Personality Traits
Researchers argued that employee's job satisfaction and job performance are influenced by many factors. These factors can be categorized as individual factors such as personality traits and locus of control, environmental factors such as supervisor and coworker support, and situational factors such as rewards. Past studies (Cheng-Liang & Mark, 2014;Raja, Johns, & Bilgrami, 2011) have suggested that personality traits might predict and play an important role in employee's job satisfaction and job performance. Dwayne (2017) argued that strong theoretical models of work behaviors based on individual differences like personality traits should be explained in the literature. Studies have emphasized various personality traits and claimed that these traits have a significant impact on one's success. Among these personality traits, Big Five traits are vastly discussed in academic literature as well as practitioners also using these traits for evaluating personality of individuals (Bhatti et al., 2014).
Although past research found positive relationship between personality traits and employees' job satisfaction and performance, researchers have ignored the role of these personality traits on diverse workforce job satisfaction and performance. Some studies have investigated the role of personality traits in the context of international HR and found that personality traits predict expatriate adjustment (Bhatti et al., 2014;Huang, Chi, & Lawler, 2005). This article argues that role of personality traits might differ when dealing with culturally diverse workforce. Therefore, there is a need to understand which personality traits play important role in multicultural environment and which type of employees gain more job satisfaction and perform better when working in culturally diverse environment.
Referring to Norman's (1963) labeling as basis, Big Five factors consist of Extroversion (sociability), Neuroticism (emotional stability), Conscientiousness, Agreeableness, and Openness to Experience, or culture. Socially active, motivated, and assertive are characteristics of individuals categorized under the Extroversion factor. These individuals regard situations where most find difficult to be opportunities and also, they often believe that all problems can be solved with hard work and perseverance. In this case, it is argued by Cheng-Liang and Mark (2014) that extroversion positively influences job performance mainly because their characteristics are often assertive, active, and sociable. In a multicultural environment, these extroversion characteristics, which are assertive, active, and sociable, might be used to help them develop positive relationships with peers, which would also provide for a better understanding of work requirements, thus setting the stage for improved job satisfaction. In addition, due to active behavior, extroverts frequently ask questions that enhance their knowledge and help them to perform better in the job. Moreover, Barrick and Mount (1991) argued that individuals with greater extroversion display positive moods and show more competencies during job which leads to higher salaries and more promotions as compared to less extrovert individuals (Seibert & Kraimer, 2001). Furthermore, Tokar and Subich (1997) suggested that individuals with stronger extroversion trait get higher job satisfaction. In addition, Paola and Antonio (2012) reported that extroversion positively related to job satisfaction. Possible reason behind this suggestion might be the wide friend circle of extrovert individuals that creates good working environment and as a result job satisfaction. Therefore, it can be concluded that individuals with greater extroversions develop good relationships with coworkers, gain more knowledge about work environment, display good mood, and show more competencies that make them satisfied with their job. On the basis of above discussion, this article suggests the following proposition: Proposition 2: Employees with extroversion traits get higher job satisfaction in multicultural environment.
Another trait in Big Five is Neuroticism factor, which has also been referenced as emotional stability or emotionality. Bhatti, Alshagawi, and Juhari (2018) stated that employees who are emotionally stable tend to predict better job performance, especially when these employees work in team. Peltokorpi (2008) have identified that individuals who are considered emotionally stable tend to feel satisfied with their job. In a multicultural environment, individuals from diverse culture tend to show different behaviors in different situations. All in all, emotional stability holds a high regard to manage and understand different behaviors, emotional stability is vital. The lack of it may result in conflicts among employees, which will ultimately create work stress and reduced job satisfaction. In this article, it can be suggested that emotionally stable employees are more likely to control their temper and handle pressure when they are placed in a culturally diverse team, which will also result in higher job satisfaction and better job performance. Therefore, based on the above discussion, this article suggests the following proposition: Proposition 3: Emotional stability positively influences employee's job satisfaction in multicultural environment.
The third dimension, which has generally been interpreted as conscientiousness, is somewhat ambiguous. Individuals with the conscientiousness trait are considered to be more responsible and reliable, careful with good in planning, and obviously hard working. It was argued by Barrik and Mount (1991) that conscientiousness is the most consistent predictor of job proficiency and positively influences job performance (Hurtz & Donovan, 2000). In addition, it was suggested by Cheng-Liang and Mark (2014) that there is a tendency for higher work commitment by individuals with conscientiousness traits. Also, it is also observed that individuals with conscientiousness traits have higher chances to achieve rewards for their work, which, in turn, create job satisfaction. Therefore, in a multicultural environment, organizations demand more responsibilities, better planning, hard work, and increased commitment from employees. As employees with higher conscientiousness possess all these characteristics, and since they are more likely to achieve rewards, it would also result in the increase in job satisfaction. In this regard, Poropat (2009) argued that individuals with greater conscientiousness are more involved in job and perform job task better than less conscientious individuals which make them receive more rewards and appreciation than others that in turn leads to better job satisfaction (Paola & Antonio, 2012). Furthermore, Andrian et al. (2009) and Furnham (2002) argued that conscientiousness is considered as a consistent predictor of job satisfaction because conscientious individuals receive more intrinsic and extrinsic rewards due to their efficient nature (Adrian, Anreas, & Tomas, 2009). In other words, it can be argued that individuals with greater conscientiousness feel satisfied with their job. Therefore, based on the above discussion, this article suggests the following proposition: Proposition 4: Employees with greater conscientiousness feel more satisfied with their job in a multicultural environment.
The fourth dimension is agreeableness, which is also often referred to as friendliness and is associated with traits that include warmth, good-natured, and tactful, but also compliant and flexible (Fazeli, 2012). Such people are more caring, empathetic, and modest, and possess altruism (Gerber et al., 2011). Apart from characteristics relating to friendliness and show of care, this dimension has also been associated with values of trust, tolerance, and forgiveness by the research community (Barrick & Mount, 1991). Cheng-Liang and Mark (2014) supported this dimension by stating that agreeableness is a highly important factor for improved social interaction. The individual with increased agreeableness tends to develop better interpersonal relationships and is able to quickly become a part of a group. In addition, it was suggested by Mount, Barrick, and Stewart (1998) that agreeableness may be used to predict job performance because individuals with high agreeableness have effective interpersonal interaction and are able to cooperate with others, thus also result in increased job performance. Therefore, it can be gathered that, in a multicultural setting, employees with a higher level of agreeableness are able to build good relationship with other employees from different cultures by their good interpersonal skills and forgiving attitude. McCrae and Costa (1991) observed that agreeableness is positively related to life satisfaction. Interestingly, similar outcomes can be obtained when life satisfaction takes the place of job satisfaction in a multicultural environment. Therefore, it can be gathered that individuals with greater agreeableness are also friendly and approachable, which, in turn, encourage them to fulfill their social needs from their job. To fulfill those social needs, they are more motivated to gain job satisfaction. Based on the above discussion, this article suggests the following proposition: Proposition 5: Employees with a higher level of agreeableness feel more satisfied with their job in a multicultural environment.
The last of the fifth dimension has been the most challenging to classify. On the basis of Norman's labeling, it is called Openness to Experience or Culture, but other researchers have referred to it as Intellect or Intelligence. Novel experiences are shared by open people (Caprara, Barbaranelli Consiglio, Picconi, & Zimbardo, 2003). Traits related with this facet contain being interested, imaginative, broadminded, enlightened, artistically sensitive, and intelligent (Barrick & Mount, 1991). In addition, Griffin and Hesketh (2004) stated that one of the more complicated personality traits is openness to experience, which actually does not strongly influence job attitude (Bruk-Lee, Khoury, Nixon, Goh, & Spector, 2009). In contrast, it was reported (Tziner et al., 2008;Paola & Antonio, 2012), due to the fact that individuals who are considered more open to experience tend to achieve more rewards, which, in turn, also experiences job satisfaction, it can be said that openness to experience positively influences job satisfaction. They are also more inclined to try new challenges and experiences, which also results in performing better at work. According to Topolinski and Hertel (2007), due to the fact that individuals who are open to experience tend to want to try new things and obviously open-minded, it can be said that openness to experience positively related to job satisfaction. However, past studies have shown contradictory findings about openness to experience. Therefore, there needs to be further research to further understand this trait. Therefore, this article suggests that a multicultural environment brings more challenges from different angles, where employees need to find ways to cope with these challenges to receive better rewards. As individuals with openness to experience traits tend to accept new challenges, they are also the ones who are better equipped to cope with these challenges in a multicultural environment and in turn, receive more rewards that eventually also set the stage for job satisfaction. Based on the above discussion, this article proposes the following: Proposition 6: Employees with greater openness to experience feel more satisfied with their jobs in a multicultural environment.

HR Practices and Diversity Management
HR professionals have been using different HR practices, including recruitment and selection, training and development, and performance appraisal and compensation, to manage employees; however, due to environmental changes and the incorporation of diversity over time, the nature of these practices have undergone various changes. Previous studies (Burbridge et al., 2002;Goodman et al., 2003) have shown that HR managers are dealing with inequalities in recruitment, training, performance evaluation, and rewards with the use of HRM toolkits that support and improve equal employment opportunities, at the same time boosting creativity in a diverse workforce. In this regard, Human (1993) argued that organizations should perform critical analysis of HR diversity practices such as recruitment, training and development, and performance appraisal and compensation. This critical analysis helps an organization to find out the areas that need improvement, overcome unfairness and discriminations, and manage diversity effectively. In this regard, Shen et al. (2009) suggested that data received from critical analysis of HR diversity practices can be compared with benchmarking in an industry or region to further improve diversity practices. Furthermore, to establish strong diversity culture, top management support is vital. Top management should make sure that company vision and mission reflect in organizational diversity policies and encourage formalization of HR diversity polices within the organization. In this regard, Kossek, Lobel, and Brown (2005) argued that diversity should be measured in the initial step of HR diversity management practices because without documented policies and record keeping, it would be difficult for organization to effectively manage and implement diversity management practices (Shen et al., 2009). The following sections will explain how different HRM practices influence diverse workforce job satisfaction and performance.

Recruitment and Selection
Among all HRM functions, one of the most important used by organizations to attract the best employees is recruitment and selection. It was argued by Cornelius (1999) that the organization can achieve a competitive edge by recruiting best people without regard of their cultural, age, gender, and personal characteristics. McCormack (2002) supports this by stating that one of the ways for organizations to gain competitive advantage is to be a proponent in the sharing of common values through recruiting and retention of people of diverse backgrounds. This seems to suggest and argue that conventional recruitment and selection process may not be suitable to organizations when its priority is to attain and manage diversity. For example, if organizational priority is to attain diversity in workforce, it could be suggested that there needs to be a new approach and perhaps construct new selection policies and procedures that support diversity needs, such as language requirement, qualification, and age. In this regard, Monga (2008) argued that to attain a diverse workforce organizations should use different recruitment and selection processes, such as advertising job positions in different languages, appearance of managers with different ethnic backgrounds in selection committees, and using techniques that show the potential of the candidates for the required position. Many organizations prefer internal recruitment in the form of internal promotions but if organizations want to maintain diversity in workforce, they should have higher diverse workforce at entry point to make sure that at the time of internal promotion, sufficient pool of diverse candidate is available for promotion. Furthermore, Shen et al. (2009) suggest that many employees perceive diversity as having equal chances to enter the organization. They further argued that even after several decades of legislation on equal employment opportunity (EEO) and affirmative action (AA), there is still a systematic discrimination in the recruitment and selection process. Furthermore, job advertisement that reflects employer preferences about diversity and antidiscrimination legislation helps to attract best candidates. In this regard, Morrison (1992) suggested that organizations with diversity management practices can develop new employment policies and cope with issues of promoting women and ethnic minorities into higher level of management. Therefore, this article suggests that when a candidate realizes that his or her employer encourages diversity, uses the best diversity management practices during the recruitment and selection process, and avoids discrimination, the level of job satisfaction will be high, which will further lead to better job performance. Furthermore, when organizations strictly follow EEO and AA legislation during recruitment and selection process, multicultural workforce perceive positive impression about organizational policies and practices, which enhances level of job satisfaction. Therefore, based on the above discussion, this article suggests the following proposition: Proposition 7: Diversity practices in the recruitment and selection process positively influence job satisfaction of a multicultural workforce.

Training and Development
Another very important HR function is training and development. This function helps organizations equip their employees with required knowledge, skills, and abilities. The objective of diversity management practices is not only recruiting diverse workforce but also retaining them. D' Netto and Sohal (1999) argued that organizations can retain employees by providing sufficient training and development opportunities. Conventional literature on training and development confirmed that training and development activities help employees to gain necessary skills and abilities that are required to perform job task so that they can enhance their job performance. As indicated in recruitment and selection, conventional ways of training and development may not be applied toward a more diverse workforce. The type of training and development should be different than conventional ones because a diverse workforce is different in terms of personality, behavior, needs, culture, and skills. In this regard, D' Netto and Sohal (1999) suggest that the use of best practices in training may be a key to effectively manage a diverse workforce. The activities include highlighting training needs linking to organizational goals, individual needs assessment, developing annual training plan, and award distribution. Therefore, it is vital that organizations systematically perform training needs assessments and based on the outcomes, design effective training programs. This is supported by Roberson, Kulik, and Pepper (2003) who stated that HR manager should carefully assess training needs and only offer training programs that fulfill the goals of the organization. Furthermore, Kossek et al. (2005) suggest that there may be some indications of employee conflict when trying to achieve diversity; however, it is the role of the external trainer involved in diversity training to help in achieving and maintaining high productivity. Shen et al. (2009) noted that most organizations design training programs based on dominant organizational culture, but the context of some diversity training may be different from actual behavior required at workplace which leads to low rate of training transfer. In other words, when diversity training contents are different from actual job task, trainees face difficulties to exhibit behaviors at workplace which they learned from diversity training. Therefore, diversity training helps diverse workforce to understand the culture, values, and norms required to perform job task effectively. Furthermore, Roberson et al. (2003) suggested that companies should explain the objective of diversity training to the employees which can either create diversity awareness among employees or develop multicultural skills. In this regard, Shen et al. (2009) argued that awareness training helps employees to understand diversity values and build social cohesion to improve individual and organizational outcomes like performance. In this regard, top-down training strategy is more effective like providing awareness training to senior manager first and team-building training at last, and all these training objectives should be linked with organizational strategic objectives. In addition, Kelli et al. (2015) stresses that a single training will not change employee behavior; therefore, it is vital that managers be aware of their possible biasness among associates and conduct diversity training on continuous basis.
Another area where discrimination is common in organizations and HR manager need to pay attention is professional development and career planning. D' Netto and Sohal (1999) argued that diverse employees often feel neglected with the perception of lack of career path. Therefore, sufficient training and development opportunities motivate diverse workforce and prepare diverse employees for future promotions. If organizations fail to address diversity issues related to development and career planning, it can adversely affect diverse workforce. In addition, equal development opportunities also deliver message among diverse workforce that their organization equally cares for employees' career development, which enhances job satisfaction and organizational commitment and reduces turnover. In other words, when employees from dominant and minority culture perceive that their organizations equally provide training and development opportunities for career development, they feel satisfied with the job which further influences job performance. In addition, when organizations dealing with multicultural workforce, equal training and development opportunities to all employees regardless of culture enhance job satisfaction. Therefore, based on the above discussion, this article suggests the following proposition: Proposition 8: When organization dealing with multicultural workforce, diversity training and equal training and development opportunity to all employees regardless of culture enhance job satisfaction of multicultural workforce.

Performance Appraisal System
The performance appraisal system helps organizations review the level of individual performance. This makes the performance appraisal system one of the main HR functions. There has been substantial research in previous literature about performance appraisal system, employee's satisfaction, and job performance. Previous literature on the area of conventional performance appraisal indicated that a fair and clear performance appraisal system helps organizations to provide a certain level of satisfaction among its employees, which would lead to increased job performance. However, it can be argued that a conventional appraisal system may not be as useful and acceptable when applied in the context of an organization with a multicultural workforce. In this context, organizations should perhaps adopt more specific performance appraisal system that is enhanced and geared to satisfy the multicultural workforce needs. As previously mentioned, it is worth considering that the performance appraisal committee should be formed to purposely represent all available cultures, races, and age groups in the organization. In support of this, Monga (2008) suggested that minorities should be included in the committee that evaluates, selects, and promotes employees, producing an effective performance appraisal system that would better suited for a diverse workforce. Also, it should be stressed that the appraisal language should focus on the performance of the employee instead of the personality. If a HR manager does not consider these elements when dealing with a diverse workforce, multicultural employees could be negatively affected (Monga, 2008). In this regard, Fulkerson and Schuler (1992) argue that culture should not affect performance appraisal system. However, in the context of 360 degree performance feedback, if supervisor and employees have similarities in culture, the chances of better performance rating will be high. In addition, organizations dealing with diverse workforce should avoid this kind of discrimination during performance appraisal process. Therefore, this article suggests that when organizations deal with multicultural employees, they should make sure performance evaluation committee represents all cultures, supervisors should not be culturally biased when evaluating subordinate performance, and performance appraisal system should not be culturally sensitive. These initiatives in the performance appraisal system in the context of multicultural setting will enhance level of job satisfaction among culturally diverse workforce. Based on the above discussion, this article suggests the following proposition: Proposition 9: Effective performance appraisal system positively influences job satisfaction of a multicultural workforce.

Compensation and Benefits
Finally, compensation and benefits is another important HR function that helps organizations to fairly distribute intrinsic and extrinsic rewards based on individual contribution toward organizational output. D' Netto and Sohal (1999) argued that good compensation system ensures direct relationship between effort and reward. Therefore, performance-based pay system is considered more effective because the rewards are measureable and linked with individual or group performance. Performance-based pay system carries multi-objectives like increasing organizational overall performance and retaining talented employees with feelings of satisfaction (Lowery, Petty, & Thompson, 1996). In this regard, D' Netto and Sohal (1999) argued that effective performance-based pay system enhances employees' job satisfaction and organizational commitment.
Past researchers have provided many evidences on the effects of compensation and benefits to employee job satisfaction; however, due to the limited literature in the context of a diverse workforce, practitioners face difficulties to understand the extent that a diverse workforce's compensation and benefit policies are similar or different to the conventional compensation and benefit policies. For this reason, Gracce (1994) stressed that inequalities of income, bonuses, and promotion affect culturally diverse workforce. Past researchers have also indicated evidences that multicultural employees experience discrimination in the amount of rewards that they receive. Kossek et al. (2005) argued that employees who are from dominant groups in the organization tend to be more satisfied with their jobs because their managers and coworkers tend to provide them with more support, along with better rewards. On the contrary, employees who work apart from the dominant group tend to be less satisfied with their job because of the inequalities they experience in rewards and the lack of support by managers and coworkers. In support of this, McLoughlin and Carr (1997) stated that job satisfaction and dissatisfaction in the context of diversity management are highly contributed by pay inequalities. In addition, when managers are dealing with multicultural workforce, it is important for organizations to fairly distribute rewards. This is because the employees' perception about fair distribution increases job satisfaction. Therefore, HR professionals should maintain pay equalities to satisfy multicultural workforce, which further helps to improve diverse workforce job performance. Based on the above discussion, this article proposes the following: Proposition 10: Equal and fair compensation system positively influences job satisfaction of a multicultural workforce.

Diverse Workforce Job Satisfaction
Researchers have highlighted many individual, organizational, and environmental indicators that have contributed to employee job satisfaction. However, they have not yet achieved a consensus on how to evaluate job satisfaction. Although past researchers have been investigating the relationship between job satisfaction and job performance, the outcomes about this relationship seem to be still unclear due to contradictory findings. Cheng-Liang and Mark (2014) reasoned that the contradicting findings referred here might be due to different individual factors that have contributed toward job satisfaction. Different researchers have suggested different dimensions to evaluate job satisfaction because of the different characteristics of the workforce. Vroom (1964) believed that job satisfaction should be evaluated based on seven dimensions including work content, promotions, organization, managers, treatment, work environment, and coworkers, whereas Smith, Kendall, and Hullin (1969) proposed that job satisfaction should be evaluated based on five dimensions such as coworkers, salary, promotions, job task, and supervisors. Furthermore, Lyons and Kashima (2003) suggested that growth and personal skills can achieve job satisfaction better than wages. Kwasi and Emmanuel (2016) argued that different individuals perceive satisfaction in different ways. Similarly, what an individual perceive as satisfactory may be considered perceivably unsatisfactory to another individual. Individual characteristics and cultural differences may be the cause of these differences in satisfaction. Therefore, the evaluation of job satisfaction has become more complex for organizations dealing with a multicultural workforce. In this regard, Bhatti et al. (2019) suggested that equal training and development opportunities, and performance-related compensation enhance employees' job satisfaction and reduce turnover. HR professionals are still struggling to understand the role of job satisfaction to diverse workforce job performance, even though past researchers have often indicated that job satisfaction is an important factor that positively influences job performance (Michita & Fredric, 2002). In this regard, Nolan (2012) reported that new challenges facing the manager who aims to enhance employee job satisfaction are due to globalization, which have contributed greatly to the significant changes in the work nature of employees. Therefore, management scholars have started to give more attention to job satisfaction (Biswas & Varma, 2012), but research related to the findings about what influences employee job satisfaction in a multicultural setting is still limited (Andreassi, Lawter, Brockerhoff, & Rutigliano, 2014). Furthermore, Malgorzata and Beata (2015) argued that, thus far, research have been limited to multiculturalism and job satisfaction. Therefore, this article suggests that psychological diversity climate, personality traits (Big Five), and HRM practices influence multicultural workforce job satisfaction (Figure 1). Based on the above discussion, this article suggests the following proposition: Proposition 11: Multicultural workforce job satisfaction positively influences multicultural workforce job performance.

Discussion
Although cultural differences among employees are still perceived to be one of the reasons for the many challenges faced by organizations, cultural differences can be properly managed to create valuable advantages to organizations. For example, it can be assumed that when multicultural employees are given the opportunity to be more involved in product development, the outcome could be products and services that are more relevant to larger consumer target, which could develop into a competitive advantage for the organization. By using effective HRM practices, the organization might be able to develop certain personality traits in a multicultural workforce to better equip them to play a more active role in the development and production process of goods and services. The employees' involvement in this process will also make them feel more important as an organizational asset, which might also lead them to being more satisfied with their job. However, there have been convincing evidences in past literature that fully explain how different HRM practices and personality traits influence job satisfaction and the performance of a multicultural workforce. Although, in a conventional setting, these factors have been explained by past researchers, the diverse nature of multicultural environment can be very much different and conventional methods are less applicable. Therefore, it is important to understand how these factors influence job satisfaction and performance in a multicultural setting. Therefore, the purpose of this article is to explain how HRM practices, personality traits (Big Five), and psychological diversity climate influence employee job satisfaction and performance in a multicultural environment.
Organizations dealing with multicultural workforce have been facing many challenges like employee conflict, discrimination and HR professionals continuously taking initiatives to deal with these challenges by selecting employees who can be trained, performing effective needs assessment at individual and organizational level, monitoring workforce demand and supply, and enhancing diversity by attracting employees from other countries. In this regard, Holck et al. (2016) suggested that HR professionals should re-evaluate HR practices to effectively deal with new challenges and make effective use of diversity opportunities. Many organizations' leadership still considers diversity practices as useless strategy and reluctant to adopt diversity practices, whereas researches have reported strong relationship between diversity practices and profit (Hayles & Mendez, 1997). Manning, Curtis, and McMillen (1996) argued that an organization with diverse culture workforce enjoys the benefits of less turnover, higher organizational commitment, and better job performance. Furthermore, past studies have also confirmed that effective diversity practices enhance employees and organizational performance (Hye et al., 2015;Madera et al., 2016). Holck et al. (2016) suggested that if diversity categories are seen as fixed and unified, HR professionals can simplify their work by tailoring diversity practices for whole groups rather than individuals. In this regard, researchers and HR professionals proposed certain best practices to manage diverse workforce. They believe that these practices help organizations manage diverse workforce more effectively, enhance employees, and ultimately, the performance of the organization (Monga, 2008;Wilson & lles, 1999). Although organizations with diverse workforce may face short-term diversity issues, such as employee conflict due to differences in culture, values, and gender, by adopting more effective diversity management practices, a diverse team can use each other's unique talents to enhance creativity and innovativeness, which would ultimately result in the organization gaining competitive advantage. In this regard, Cox and Blake (1991) added that organizations can enjoy other advantages such as reducing turnover, absenteeism, and attract the best employees if a multicultural workforce can be managed effectively. D' Netto and Sohal (1999) argued that effective management of diversity leads to development of skills and the creation of policies that would encourage employees to reach at their maximum potential and thus achieve organizational goals. Therefore, it is vital for organizations to have a proper and effective integration of diversity practices in pay, appraisal, recruitment and selection, and training and development. Furthermore, the best use of these HR practices helps organizations to satisfy and enhance their multicultural workforce job performance.
Past researchers have investigated the impact of personality traits on job satisfaction and performance in various settings and found varied results. For example, Bostjancic (2010) found that managers with greater emotional stability can be a predictor for higher job satisfaction. Similarly, Foulkrod, Field, and Brown (2010) found that emotional stability can also be a predictor for job satisfaction among trauma surgeons. Templer (2012) also studied the relationship between personality traits and job satisfaction in Asian societies and identified that the traits agreeableness, emotional stability, extroversion, and conscientiousness are predictors for job satisfaction. Mount et al. (1998) also claimed that personality traits affect employee job performance. Personality measures can be the predictors of job performance (Barrick & Mount, 1991). In contrast, Judge, Eriz, Bono, and Thoresen (2003) had slightly skewed results indicating the traits neuroticism, conscientiousness, extroversion, and agreeableness to be positively related to job satisfaction; however, openness to experience showed a weak relationship with job satisfaction. In addition, Cheng-Liang and Mark (2014) conducted a similar study among the employees in banks in Taiwan, which examined the influence of personality traits on job satisfaction and performance and reported that agreeableness is the most influential trait, whereas extroversion is the least influential personality trait toward job satisfaction and performance of its employees. Chet, Douglas, and Paul (2005) investigated the influence of personality traits on job performance of U.S. and Japanese managers and reported that U.S. managers placed extroversion as less important for job performance whereas Japanese managers place agreeableness as less important for job performance. Both U.S. and Japanese managers place equal importance to emotional stability for job performance. In contrast, U.S. managers placed conscientiousness and openness to experience on higher score as compared to Japanese managers. This concludes that personality traits influence employee's job performance and satisfaction differently in different culture.
Past researches have investigated relationship between personality traits and job satisfaction, but findings of these studies are not consistent (Bhatti et al., 2018;Mazler & Renzl, 2007;Mount et al., 1998;Tziner et al., 2008). In this regard, IIies, Scott, and Judge (2006) proposed that researchers need to further explore the role of personality traits in job satisfaction to better understand this relationship. Based on the literature review, this article concluded that past researchers have ignored the examination of personality traits toward job satisfaction and performance in multicultural setting. Examination of personality traits predicting multicultural workforce job satisfaction and performance is vital to understand the role of personality traits in multicultural setting.
How employees perceive the organization's policies and procedures plays a monumental role in creating satisfaction at job and enhancing performance. When employees hold a common perception that their organization supports diversity and rejects cultural discrimination, this would create a psychological diversity climate that improves employee job satisfaction and performance. Maryam, Bader, and Mohd (2017) stated that employees external to the dominant culture often feel ignored and face discrimination in the organizations dealing with multicultural workforce. In this regard, when organizations implement effective EEO/AA policies, employees outside dominant culture also gain fair rewards which create satisfaction among multicultural workforce. Shore et al. (2009) highlighted that organizational initiatives toward formal diversity policies and procedures can be considered as a starting point toward creating positive organizational environment for employees. All in all, antidiscrimination policies, fair distribution of rewards, and formal EEO/AA policies produce a positive psychological diversity climate that enhances job satisfaction and performance among multicultural workforce.

Implications and Future Research Directions
This article suggests a number of theoretical and practical implications. From a theoretical point of view, this article solidifies the body of knowledge by clearly explaining the role of the psychological diversity climate, HRM practices, and personality traits (Big Five) in the job satisfaction and performance of a multicultural workforce. It is worth to note that past studies have not highlighted the role of the psychological diversity climate in multicultural setting. Employee's cognitive judgment depends on organizational environment and culture. If organizations practice certain policies that encourage diversity, where multicultural employees are given the opportunity to freely express their opinion and contribute, employees would perceive that their organization provides support for diversity and a multicultural environment. Understanding different cognitive factors that build positive employees perception about organizational climate is important for researchers. Therefore, psychological diversity climate explains that employees develop their perception from organizational environment and researchers should highlight other factors that develop employees perception toward organization climate. These arguments are aligned with social cognitive theory which explains that employees act based on psychological climate and external environmental factors create psychological climate. Therefore, diverse organizational policies, procedures, and practices, when properly implemented, can develop a positive psychological diversity climate, which could positively influence multicultural job satisfaction and performance. Future research should perhaps highlight other individual and organizational factors, which might help employees gain a psychological diversity climate.
With reference to HRM practices, social exchange theory suggests that individuals feel satisfied or dissatisfied based on exchange of reward/punishment. For example, employees in multicultural setting expect that organization will offer diversity training and equal opportunities for training and development to help employees to develop good career path and feel comfortable in multicultural environment. In exchange, employees exhibit satisfactory feelings related to job which influence job performance. Similarly, employees exhibit satisfactory behavior in exchange of organizational diversity practices like recruiting multicultural workforce, avoiding discrimination, developing formal diversity polices, equal distribution of rewards and effective compensation policy, unbiased appraisal system, and follow EEO/AA legislation. Through the understanding of social exchange theory and placing it in the context of HRM practices, researchers may be able to better conceptualize the nature and scope of these practices in a multicultural setting. Perhaps then, researchers should be able to clarify the roles of other HR practices in multicultural contexts such as in health and safety, and industrial relation.
Personality traits (Big Five) were derived from trait theory which explains that individuals hold different traits and act differently in similar situation. This article further elaborates on personality traits and their link with cultural factors highlighted by Hofstede. Conceptualization of personality traits in the context of different cultural dimensions will help researchers to understand how individuals with different personality traits respond to different situations in different cultures. This article explains these phenomena and theoretically links personality traits and cultural dimensions, which will further strengthen the theoretical boundaries. Sufficient explanation of these traits in a multicultural setting should help researchers understand how each personality trait operates in a multicultural setting and influences employee job performance and satisfaction. Future researchers should be able to highlight other personality traits, such as self-efficacy, locus of control, and self-esteem. Once these traits have been identified, researchers may be able to explain how these personality traits influence job satisfaction and performance in a multicultural workforce.
In addition to theoretical implications, this article also suggests many practical implications as well. First, this article suggests that managers and HR professionals should focus on creating psychological diversity climate in the organization by using different strategies such as participation of culturally diverse employees in developing organizational policies, incorporating equal employment opportunities message in the mission and vision statement of the company, clear antidiscrimination legislation, representations of employees from minorities in the management, and cultural festivals. These initiatives will send a strong message to the mind of the employees that their organization encourages and supports diversity, that all employees are treated equally regardless of their culture, ethnicity, or gender. This would help create a positive psychological diversity climate.
Second, top management and HR managers should craft their HR practices carefully by considering needs of each employee. For example, managers should ensure that the organization's job advertisements are made in different languages, which would effectively deliver a diversity-related message to the prospective applicant. Recruitment and selection committee should consist of diverse members representing different cultures; selection criteria should be universal rather than representing specific cultural norms and values. Evaluation of each candidate should be based on certain criteria rather than on their cultural affiliations. In addition, training may be an effective vehicle to create diversity awareness. Managers can integrate diversity elements in employee training to not only create awareness among multicultural employees but also to clarify relevant expected behaviors required at workplace. This will help employees to understand the other cultures, and they will display expected behavior which will make them feel satisfied at job. Furthermore, offering equal training and career development opportunities regardless of their affiliations and cultural background can help them to feel satisfied and perform better at workplace. The reason behind this approach is that employees with similar culture may not need certain training due to cultural similarities or similar education system or working style. When employees from different background work together, their training and development needs might differ. Therefore, HR managers should identify training needs of other employees and provide training accordingly. Furthermore, managers should put together performance appraisal teams that represent different cultures so as to prevent feelings of discrimination among multicultural employees. This will also encourage employees outside dominant culture to play more active roles in organizational development.
Finally, this article suggests specific strategy to deal with different personality types and cultural dimensions. HR manager should carefully evaluate the type of culture in which organization operates. Then, he or she should carefully examine which type of personality trait is required in that culture. Even in hiring prospective employees, HR managers should evaluate prospective employees' personality and select those who possess personality traits that include agreeableness, emotional stability, and extroversion. This is because, as indicated in this article, employees with these traits create a positive work environment, because they tend to accept challenges, and are more assertive and active, which also create for themselves a feeling of satisfaction in multicultural setting and perform better. All in all, the selection of employees with these traits or training toward developing these traits will be useful for managers to achieve their set targets.

Declaration of Conflicting Interests
The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding
The author(s) received no financial support for the research, authorship, and/or publication of this article.


extfieldsofstudy:
Computer Science
Medicine

s2fieldsofstudy: Business Education

text:
From choice architecture to choice engineering

Qualitative psychological principles are commonly utilized to influence the choices that people make. Can this goal be achieved more efficiently by using quantitative models of choice? Here, we launch an academic competition to compare the effectiveness of these two approaches.

The Q-learning model is a reinforcement learning algorithm that has been widely used to model sequential decision-making behavior in humans and animals [1][2][3] . Applied to this task (formally a one-state MDP), Q-learning describes how the value (expected average reward) associated with each action changes in response to that trial's chosen action and the resultant reward. Formally, at each trial t, the agent selects an action , ∈ {1, 2} and receives a reward , ∈ {0, 1}. The updated value of the selected action, +1 ( ), is a weighted average of the previous value ( ) and the received reward: (1) +1 ( ) = ( ) + ( − ( )) where 0 < ≤ 1 is the learning rate. The value of the nonchosen action remains unchanged, +1 ( ≠ ) = ( ≠ ). The difference equation (1) is not complete without specifying the initial conditions. Following experimental findings, we posit that in the first two trials the two alternatives are chosen at random and the initial value of each of the two actions is the reward received the first time this action was chosen 4 .
Equation (1) describes how the action values adapt over trials but does not specify how these action values are used to select actions. The mapping between action-values and actions is given by an action-selection rule. Motivated by experimental findings 4 , we consider an -softmax action-selection rule such that: where 0 ≤ ≤ 1 and > 0 are exploration parameters.
Together, Eqs. (1) and (2) 4 , is equal to the same product in the current problem.

The CATIE model
The contingent average, trend, inertia, and exploration (CATIE) model is a phenomenological model developed to explain human behavior in tasks of sequential choices with partial feedback, similar to the task of the competition 5 . The model describes an agent which in each trial, chooses according to one of four modes: exploration, exploitation, inertia, and a simple heuristic. In the first two trials, the agent samples the two alternatives in a random order. In each consecutive trial, one of the four modes is selected according to the following probabilistic rules: 1. If the agent chose the same alternative in two consecutive trials and their outcomes differed, it would choose in the subsequent trial the trend (or heuristic) mode (see below) with a probability . 2. If the trend mode was not chosen, the agent would choose the explore mode (see below) with a probability p_explore. 3. If neither trend nor explore modes were chosen, the agent would choose, the inertia mode (see below) with a probability . 4. If none of the above modes was chosen, the agent would choose the contingent average mode (see below).
In the trend mode, the agent would choose the same alternative as in the previous trial if the trend of last two outcomes was positive, i.e. if the last outcome was greater than the one preceding it. If the trend was negative it would switch to the other alternative: Where , = {1, 2} are the available alternatives in the task, is the action at trial (i.e. the choice of 1 or 2 ) and ∈ {0, 1} is the reward at trial . In the context of the competition (binary rewards), trends are manifested by a sequence of either reward no reward (negative trend), or no reward reward (positive trend).
In the explore mode, the agent chooses between the alternatives randomly, with an equal probability. The probability of entering the explore mode is a function of the sequence of surprises experienced by the agent up until the current trial. Surprise ∈ [0, 1], is calculated at trial as follows: Where Exp is the reward the agent expects to receive at trial after choosing alternative at trial (the alternative's contingent average, see below), is the actual reward obtained by choosing alternative at trial , and ObsSD is the standard deviation of all payoffs observed from alternative at trials 1 through . Note that at each trial the surprise is calculated relative to the single alternative chosen by the agent. Given the sequence of previous surprises, the probability of entering the explore mode, conditioned on not choosing the heuristic mode is: Where is a free parameter capturing a basic exploration tendency and Mean_Surprise is the average surprise in trials 1 through . Thus, the probability of exploration is minimal (equals 3 ) when the surprise is minimal (both Surprise and Mean_Surprise equal 0), and maximal (approaches ) when the surprise is large.
The inertia mode simply repeats the same choice of the previous trial.
In the contingent average (CA) mode, the agent chooses the alternative associated with the higher k-CA, defined as the average payoff observed in all previous trials which followed the same sequence of k outcomes (the same contingency of length k). At its initialization, the agent uniformly draws an integer from the discrete range {0, … , } (~{0, }, is a free parameter). Each time the agent enters the CA mode, it calculates k-CA for the two alternatives. For each alternative , k-CA is the average reward obtained in trials which followed a contingency of length which is identical to that of the most recent -contingency and were followed by choice of . In particular, =0 implies averaging all the outcomes of an alternative. To illustrate this process, consider the following sequence of 10 choices in alternative 1 ("A") and 2 ("B"): [A, A, A, A, A, A, A, B, B, B], implying the agent is currently at the 11th trial, and assume that these choices yielded the following reward sequence [1, 0, 0, 0, 1, 0, 0, 1, 0, 0]. An agent characterized by a =2 would imply that the current contingency is [0, 0] (the sequence of last two rewards). Previous indices where the same reward sequence was observed are 2, 3 and 6; the choices which followed these sequences are A, A and B respectively (at trials 5, 6 and 9); and the rewards which followed these contingencies are 0, 1 and 1 (the rewards of trials 5, 6 and 9). This would imply that the contingent averages of alternatives A and B are 0.5 and 1 respectively. Hence, in the current trial alternative B, which has the higher contingent average, would be chosen. If for alternative there are no past k-contingencies matching the most recent contingency, the value of a different random kcontingency replaces the contingent average for that alternative. A random k-contingency value is obtained by considering the set of all reward sequences of length which were followed by choice of , randomly choosing one of them with a uniform probability and calculating its contingent average value. Note that choosing uniformly from past trials implies that recurring contingencies have higher probability of being chosen. If there are no contingencies of length that are followed by a choice of , a smaller k (k:=k-1) is chosen iteratively until at least one contingency exists. Since the model is defined to sample the two alternatives in the first two trials, for k=0 it is guaranteed that both alternatives would have a 0contingency value and hence that the CA mode is well defined.
As described above, the model is characterized by four free parameters (one for each mode: , , , ). The parameters of the model were estimated from behavior 5 and these estimations were used in all simulations: = 0.29, = 0.30 , = 0.71, = 2.

Finding an optimal static reward schedule
The optimization procedure operates iteratively. In the first iteration, an initial sequence 1 is generated by randomly shuffling, independently for the two alternatives, a sequence that complies with the global sequence constraints (rewards are assigned to 25 of the experiment's 100 trials). In the 'th iteration, a partially reshuffled sequence ′ is generated from the current sequence by choosing ~{2, } indices, with uniform probability without replacement, independently for the two alternatives, and randomly reshuffling the rewards assigned to the trials of these indices. The schedule ′ is tested times ( independent agents) and compared to the bias previously obtained for the unshuffled schedule. This procedure is repeated times and the schedule used for the subsequent iteration is the one that yields the largest bias out of the + 1 tested schedules ( shuffled schedule + the original schedule). The variable , which represents the 'temperature' of the algorithm progressively decreased to zero such that = ( ), are parameters. The parameters we used for this procedure are = 10,000, = 100, = 500, = 10. Finally, we note that the reward of the last trial cannot change behavior. Hence, it is never advantageous to allocate a reward to the last trial of the biastarget alternative. If the stochastic optimization converges to a solution which does not meet this criterion, the reward schedule of the bias-target alternative is modified to conform with this heuristic by reallocating the reward of the last trial to a random trial currently not associated with a reward. Similarly, if a reward is not assigned to the last trial of the anti-bias alternative, one of the rewards associated with that alternative is randomly chosen and reallocated to the last trial.
Note that this method is not guaranteed to find a global optimum, nor to converge to the same solution in independent applications. Therefore, we repeated this procedure = 20 times and chose the schedule that yielded the maximal bias. To avoid selection bias, the bias measured in Fig. 2 was measured by simulating the schedule on 1,000 independent agents.

Finding an optimal dynamic reward schedule
We used an artificial neural network to dynamically allocate rewards to the two alternatives. In each trial, the network receives an input which encodes the history of past choices and rewards (see also below), and its output is the allocation of reward to each of the alternatives in that trial. To guarantee that the constraints are satisfied, the network could not assign additional rewards to an alternative in which 25 rewards have already been assigned. Similarly, if the number of remaining trials is equal to the number of remaining rewards, a reward is assigned in every trial until the end of the session.
The network is composed of four layers 0 , 1 , 2 , 3 . The activity of neuron in layer > 0, is given by: where is the number of neurons in layer and is the strength of connection from neuron in layer − 1 to neuron in layer .
The number of neurons in layers 1 and 2 is 1 = 2 = 100. The output layer is composed of four neurons ( 3 = 4). Each of the four neurons denotes a particular allocation of rewards (no rewards, reward only to alternative 1, reward only to alternative 2, rewards to both alternatives) and the allocation of rewards is determined by the identity of the most active neuron in that layer.
The weights were trained iteratively using a genetic algorithm 6 .
In each iteration (generation) ten sets of weights were generated. The performance of each of the ten sets of weights was evaluated by estimating the average bias associated with that set of weights, as was done for the static reward, and the two sets that yielded the largest bias were identified and used for the construction of weights for the next iteration. The ten sets of weights were constructed in the following way: one set of weights was chosen from a uniform distribution, ~(−0.05, 0.05), two more sets of weights were the two best performing sets of the previous generation, denoted as parents of the current generation. Seven more sets of weights were constructed using a crossover procedure, in which each weight is independently drawn from one of the parents' sets of weights. Finally, each of the weights were 'mutated' in a probability of 0.2. A randomly drawn number from a uniform distribution Δ~(−0.005, 0.005), independently drawn for each weight and each set was added to each mutated weight. This procedure was terminated when the improvement in bias, relative to the average of the last 400 generations, was smaller than 0.01. The input layer 0 depended on the model used.
When constructing a dynamic reward schedule for the QL model, the input layer was composed of four neurons whose activity in every trial denotes (1) trial number; (2, 3) total number of reward allocated in previous trials to alternatives 1 and 2; (4) the difference between the two alternatives' Qvalues, ( 1 ) − ( 2 ), as estimated from previous trials using the true parameters of the model. When constructing a dynamic reward schedule for the CATIE model, the input layer was composed of six neurons whose activity denotes (1) trial number; (2, 3) total number of reward allocated in previous trials to alternatives 1 and 2; (4) an indication for current trend represented by the values: −1 if trend is not applicable (if two previous actions are not identical), 0 if the trend is negative, and 1 if the trend is positive; (5) the probability of using the exploration mode (p_explore for the explore mode); (6) the alternative chosen in last trial (for the inertia mode).

Sorting applications with 'successive-rejects'
Consider a reward schedule submitted to the competition. If tested over different subjects, it is likely to yield a different bias for each subject. This is due to stochasticity in the behavior of the individual subject and the heterogeneity between the subjects. In this sense, the reward schedule defines a distribution of biases over subjects, and our goal is to identify the reward whose distribution is associated with the largest mean. Successive-rejects 7 is a method for an efficient allocation of a finite number of draws (subjects) from distributions (schedules) to optimally identify the distribution with the highest mean. Successive-rejects operates iteratively. In the first iteration, all distributions are sampled. In each iteration, the distribution associated with the lowest mean (as estimated from all draws up to this point) is removed from the set of considered distributions and the remaining distributions are reevaluated by drawing a specific number of additional samples each. In order to compute the number of draws used in iteration for each of the remaining distributions, we denote by the cumulative number of draws from that distribution up to iteration (included). By definition, 0 = 0 and − −1 is the number of draws used in iteration per each remaining distribution. According to the method of successive rejects, The algorithm terminates after − 1 iterations, when only a single distribution (schedule) remains.


Research on the Relationship Among Pay Equity, Employee Engagement and Job Performance

Companies at the same time of saving the cost of human resources, how to grasp in saving the cost of human resources and the balance of salary incentive, is difficult to solve problems, in the economic development in the new period, the study of the balance of cost and salary incentive is guarantee the important theoretical problems of human resources, introduce professional model, study the effect of different compensation fairness on work performance mechanism. The group engagement model divides employee behavior into mandatory behavior and autonomous behavior. Combining with comprehensive work performance, it divides work performance into task performance and relationship performance, and explores the influence mechanism of employee engagement on work performance. The group engagement model integrates the mechanism of social identification and the mechanism of resource exchange, and holds that the three different types of equity affect work performance by influencing employee engagement. The fairness of compensation procedure will not affect employees' cognitive engagement, but it will play a positive role in improving employees' emotional engagement and behavioral engagement. Compared with procedural justice and distributive justice, the salary communication justice has a stronger positive effect on employee engagement.

Introduction
Due to the lack of effective incentive mechanism in some enterprises in management practice, there is a lack of recognition of salary equity, and employees are slack in their work. In the new era of talent competition, it is necessary to re-study the relationship between fair cognition and effective incentive mechanism, so as to stimulate employees' enthusiasm and improve individual performance and enterprise benefit. Kahn(1990) proposed the concept of engagement, pointing out that engagement refers to the degree to which organizational members combine their own factors such as personal emotion, ability and other resources with their work roles in the work process. Sun weimin and lu cui (2012) defined employee engagement as a positive, work-related psychological state and behavioral performance, including employees' recognition of the sense of value and meaning of work, their sense of mission and pride in work, and their willingness to make extra efforts for the success of the organization. Hardaker and Fill(2005) distinguish employee engagement from the perspective of rationality and sensibility. Among them, rational engagement mainly refers to employees' efforts and inputs in work after they fully understand the possible efforts and gains in the work process, while emotional engagement mainly refers to employees' attention and enthusiasm for their work roles. Qian Aimin etc. Studies show that distributive justice is the rights of the employees' work pay cash to the fundamental principle and basic way, if employees perceive business pay to allocate unfair or fair degree is low, its work enthusiasm will be contusion, leading to slack off or leaving out inner discontent expressed the unfair distribution of compensation, work efficiency is low.
The above research, based on work performance, explores the positive effects of salary equity and employee engagement, and evaluates employee work performance from a single dimension, which cannot accurately reflect the characteristics of current employee work and the positive effects of salary equity and employee engagement. Therefore, combining with the group engagement model, this paper evaluates work performance from the two dimensions of task performance and relationship performance, and explores the positive effects of salary equity and engagement, which are of great value. In addition, there are existing literatures on the effect of salary equity and engagement, but few researches explore the change rule of its action mechanism based on the individual characteristics of employees. This paper studies the differentiation of the positive effect based on the difference of employees' emotional intelligence.

Group Engagement Model 2.1. Group Engagement Model Concept
The group engagement model was developed by Tyler and Blader (2003) as a theoretical model to explain the collaborative behavior of team members. Based on the relationship model of authority and the group value model, the theoretical model puts forward a new research category. Expand the perceived role of fairness from employees and leaders to group members; The model clarifies the mechanism of the influence of fairness on group engagement and cooperative behavior, namely the mechanism of social identity and the mechanism of resource exchange. The judgment of procedural fairness in the process of organizational management comes from four factors: the quality of formal decision-making, the quality of formal interpersonal treatment, the quality of informal decision-making and the quality of informal interpersonal treatment. The fairness of salary procedure reflects the formal and informal factors of decision quality, while the fairness of salary communication reflects the formal and informal factors of interpersonal treatment quality. When employees perceive a high degree of procedural and interpersonal justice in the process of salary distribution, their perception of organizational justice will be strengthened, thus facilitating the switch from individual identification to group identification, and ultimately improving their engagement level.

Analysis of the Relationship between Salary Fairness and Employee Engagement
Compensation is one of the main resources that employees get from the organization, and it is also the human resource management module that employees value most and affects almost everyone. Organizations can not only through the distribution of compensation to achieve the exchange of resources with employees, also can through the different ways of compensation distribution, release different signal to employees, and guide the staff's cognition, attitude and behavior (Meyer, Dalai & Hermida, 2010) pay distribution has been an important fair research situation, the scholars from the initial attention only fair pay distribution, gradually extended to the program and fair, and many other areas of concern. The most typical example is the study of Triwibowo (2016), which explored the mechanism of the effect of salary equity on employee engagement from the three dimensions of distributive justice, procedural justice and communication justice.
According to the group engagement model, the influence of fair salary distribution on employee engagement is first realized through the resource exchange mechanism and then through the social identity mechanism, while the resource exchange emphasizes reciprocity and reciprocity in the exchange process. The so-called equivalence means that the investment difference between the two parties in the exchange process cannot be too large and the two parties are in the equivalence relationship. Only in this way can the exchange parties form a good social exchange relationship rather than a simple economic exchange. Employee engagement is a high investment provided by employees to the organization, because high employee engagement promotes employees to invest their own resources in time, energy and other aspects (Qiu min, Hu luo, 2015).

Three Dimensional Model Relationships
Taking salary equity as the antecedent variable, individual work performance as the outcome variable, employee engagement as the mediating variable between salary equity and individual performance, and individual employee emotional intelligence as the moderating variable, a conceptual model including salary equity, employee engagement, work performance and employee emotional intelligence was constructed. This model mainly tests the relationship and function logic between the following concepts: first, the correlation between salary equity and employee engagement; Secondly, the correlation between employee engagement and job performance; Thirdly, the correlation between salary equity and job performance; Fourth, the mediating role of employee engagement between salary equity and job performance; Fifth, the regulating effect of emotional intelligence.

Research Design and Data Collection 3.1. Survey Design
Data and data on employee compensation equity, employee engagement and employee performance are collected through questionnaires. The design of the questionnaire mainly includes the following steps: Firstly, on the basis of combing the relevant literatures at home and abroad, the scales published in the top journals at home and abroad have been selected and have good reliability and validity. The translation of the English scale is generally accepted. The reverse translation method; secondly, based on the formed scale for field interviews and pre-study, the purpose of the pre-study is two, one is whether the statement of the item is clear enough and accurate, and can make the respondent easy to understand And answer and check, and accept the opinions of the respondents to correct the way of expressing individual problems; second, based on the data obtained from the survey, carry out preliminary reliability and effect test, verify the scientific nature of the questionnaire design, form a formal basis survey. The questionnaire mainly includes the following three parts: (1) Fill in the questionnaire. This section mainly introduces the purpose and main content of the questionnaire, and introduces the respondents to how to correctly fill out the questionnaire. In order to improve the efficiency of the questionnaire, in this section, the respondent is promised that the survey is only used for academic research. It is definitely not for commercial use, and the situation of the respondents is kept confidential, so that the respondents can answer with confidence.
(2) Basic information of employees and companies. This part mainly conducts basic investigations on the personal information and company information of the respondents as the control variables in the empirical analysis. The questionnaire mainly covers the age and gender of the respondents.
(3) The measurement items of the key variables involved in this paper. The variables involved in this study include the three dimensions of pay equity, fairness, procedural fairness, and fairness of communication. The three dimensions of employee engagement are cognitive dedication, emotional dedication and behavior. .

. Sample Structural Description
After the questionnaire was collected and collated, there were 309 valid questionnaires. The gender distribution was as follows: 165 males and 144 females, accounting for 53.40% and 46.60% respectively.
In the questionnaire, based on whether the company belongs to the high-tech industry, the respondents were investigated. The result is that the majority of the 207 respondents are in the high-tech industry, accounting for 66.99%, and the company is the company. There were 102 investigators, accounting for 33.01%. The distribution of the industry matches the overall academic qualifications of the respondents and is relatively high.

Correlation Analysis
Some assumptions about the relationship between pay distribution fairness and employee engagement and job performance have not been verified. Through theoretical deduction, this paper proposes that the fairness of salary distribution is conducive to improving employee engagement and job performance. However, based on the empirical analysis of the data obtained from the questionnaire, it is found that the relationship between salary distribution and employee emotional dedication, behavioral dedication and employee performance is Did not pass the significance test.
Secondly, although emotional intelligence can significantly regulate the relationship between salary communication fairness and behavioral dedication, it has no significant effect on the adjustment of salary communication fairness and cognitive dedication and emotional dedication. The reason for the analysis may be that the task performance is the behavior of the employee, and the evaluation system is relatively perfect. Under the premise of clear objectives, the influence of the eccentricity of emotional intelligence is not obvious, but the relationship performance is the behavior outside the role, and the completion process requires the subjective of the employee. Motivation, the path of interaction fairness to relationship performance will be significantly affected by changes in the external environment.