What is game theory?
Game theory is a framework for understanding social events with competing actors. Game theory studies optimum strategic decision-making by independent and competing agents.
Various areas employ game theory to explain situations and anticipate their likely outcomes. It may help companies establish pricing, decide to acquire another, and handle lawsuits.
How Game Theory Works
In a setting with rules and consequences, game theory studies the strategic activities of two or more “players.”If two or more players have known payments or measurable effects, game theory may help us predict the most likely outcomes.
Game theory focuses on games as models of rational player interactions. Game theory states that one player’s payout depends on the other’s strategy.
The game reveals participants’ identities, preferences, and strategies, and how these impact the outcome. Other assumptions or needs may depend on the model.
Psychology, evolutionary biology, military, politics, economics, and business use game theory. Game theory is continually growing despite its significant breakthroughs.
Game theory states that all participants’ actions and decisions impact each other’s results. One assumes game players are rational and will maximize their payoffs.
Useful Game Theory Terms
Game theory terminology includes:
- A game is any situation where the outcome depends on the actions of two or more decision-makers (players).
- Players: A strategic decision-maker in the game.
- Strategy: A comprehensive plan of action for a player to follow in a specific game scenario.
- The compensation a player receives for achieving a specific outcome The reward might range from money to utilities.
- The information set: The current game information Sequential games commonly use the phrase information set.
- A game reaches equilibrium when both players make decisions and establish an outcome.
In the 1940s, mathematician John von Neumann and economist Oskar Morgenstern pioneered game theory. Mathematician John Nash may be considered a significant extension of their work.
Nash equilibrium is an outcome where players cannot unilaterally change their decisions to improve rewards. It’s also synonymous with “no regrets,” since the player won’t regret their choices after weighing the repercussions.
Most Nash equilibriums occur over time. Once attained, the Nash equilibrium cannot be changed. After finding the Nash equilibrium, consider the effects of a unilateral maneuver. Does it make sense? It shouldn’t. Thus, Nash equilibrium is “no regrets.”
In general, games have several equilibriums. More sophisticated games than two options by two players frequently include this. Trial and error leads to one of these numerous equilibria in repeated simultaneous games.
When two companies set pricing for highly interchangeable items like flights or soft drinks, this scenario of different options over time until achieving equilibrium is most common.
Game Theory Impact
Game theory is used in most industries and research fields. Its broad principle applies to many circumstances, making it adaptable and vital to understand. Game theory affects these subjects.
Game theory revolutionized economics by solving key mathematical economic model issues. For example, neoclassical economics grapples with entrepreneurial anticipation and imperfect competition. Game theory shifted the focus from steady-state equilibrium to markets.
Economists utilize game theory to analyze oligopoly corporate behavior. It aids in predicting results from actions like price-fixing and cooperation among corporations.
Game theory helps businesses model economic competition. Businesses face several strategic decisions that impact their profitability. Also, businesses may have to decide whether to retire old items, create new ones, or use new marketing methods.
Businesses typically pick their opponent. Some compete with market participants and focus on external influences. Others want to improve themselves. Companies compete for resources, employ the finest individuals, and steal clients from internal or external competitors.
The game tree below may best represent corporate game theory. Starting at position one, a firm must choose two outcomes. However, there are always more selections, and the exact compensation amount is unknown until it is processed.
Project management incorporates social game theory, as individuals may have varying impacts. Incentives may motivate a project manager to finish a construction project. Incentives may encourage construction workers to work slower for safety or delay the project to increase billable hours.
Game theory may be less prominent in internal teams since all employees are more interested in success. The success of a project may not incentivize third-party consultants or other parties.
Pricing Consumer Goods
The strategy of Black Friday shopping is essential to game theory. Pricing reductions encourage buyers to buy more things. Game theory focuses on the interaction between a customer, a good, and the financial exchange to transfer ownership since consumers have various expectations.
Companies should use game theory to price items for launch or anticipate competition beyond pre-holiday sales. Finding balance is essential. Pricing a product too cheap may not generate profit, while pricing it too high may make clients consider alternatives.
Types of Game Theories
Cooperation vs. Non-Cooperation
Several game theories exist, but cooperative and non-cooperative are the most prevalent. Cooperative game theory studies coalitions’ interactions when only payoffs are known. Playing this game between coalitions of players rather than individuals explores group formation and payment distribution.
To attain their aims, rational economic actors interact in a non-cooperative game. Strategic games, which list just strategies and their results, are the most prevalent non-cooperative games. Rock-paper-scissors is a simple, non-cooperative game.
Zero Sum vs. Non-Zero Sum Games
A struggle between numerous parties pursuing the same objective is a zero-sum game. For every winner, there is a loser. Alternately, the aggregate net gain obtained equals the loss. Many sports are zero-sum games.
All players can win or lose in a non-zero-sum game. Choose business alliances that benefit both parties. Instead of trying to “win,” both parties profit.
Stock investing and trading can be zero-sum. One market player buys a stock and another sells it for the same amount. However, investors have varied risk tolerances and investing goals, so transacting may benefit both parties.
Games with simultaneous and sequential moves
In life, game theory often appears in simultaneous-move scenarios. This implies that each player must make decisions as their opponent does. Competitors do the same as organizations create marketing, product, and operational strategies.
Some parties intentionally stagger decision-making processes to watch others’ movements before making their own. Negotiations often involve one side listing requests, followed by a predetermined period for the other party to react and list their own.
One-shot vs. repeated games
One case can start and terminate game theory. Like most things in life, the competition begins, advances, and ends. Equity traders must carefully select their entry and exit points because they cannot reverse or retry.
However, some repeated games never stop. These games usually involve the same players who know what happened last time. Consider competing firms pricing their goods. One may change prices when the other does. Circular competition repeats over product cycles or sales seasons.
The example below shows the Prisoner’s Dilemma (explained next). This illustration shows little benefit after the first repeat. Instead, a second game iteration brings fresh outcomes not attainable in one-shot games.
Game Theory Examples
There are various “games” that game theory analyzes. Below, we briefly describe many.
The most famous example of game theory is the Prisoner’s Dil emma. Consider two arrested criminologists. Prosecutors lack proof to convict. However, officials remove convicts from their isolated cells and interview them individually to get confessions. Neither prisoner can communicate. Officials display four transactions in a 2-by-2 box.
- Both may spend five years in prison if they confess.
- P1 will get three years and P2 nine years if he confesses, but P2 does not.
- Should Prisoner 2 confess but Prisoner 1 does not, Prisoner 1 will receive 10 years and Prisoner 2 two years.
- Without confession, everyone will serve two years in jail.
Avoiding confession is best. Neither knows the other’s method, so both will likely confess and receive a five-year term.According to Nash equilibrium, in a prisoner’s dilemma, both parties will do what’s best for them individually but worst for them together.
“Tit for tat” is the best prisoner’s dilemma tactic. Anatol Rapoport proposed tit for tat, a strategy in which each player in an iterated prisoner’s dilemma follows their opponent’s previous turn. A provoked player retaliates; an unprovoked player cooperates.
The graphic below shows a situation where the column and row participant choices conflict. If both parties chose row or column 1, they may benefit most. Each person risks severe negative repercussions if the other person chooses a different result.
Simple game where Player A decides how to share a financial award with Player B, who has no say. Although not a game theory method, this approach offers intriguing insights into human behavior. In experiments, 50% keep all the money, 5% split it evenly, and 45% share it at a lower percentage.
Like the ultimatum game, the dictator game involves Player A giving Player B part of a specified sum of money, which he might accept or refuse. Both A and B lose if the second player refuses the offered sum. The dictator and ultimatum games provide valuable lessons for charitable giving and charity.
In a volunteer’s dilemma, someone must do charitable work. No one volunteering is the worst consequence. Take the example of a corporation where accounting fraud is prevalent but upper management is clueless. Junior accounting staff may be aware of the fraud but fear reporting it to management to avoid potential repercussions, such as termination and prosecution.
Labeling someone as a whistleblower may have long-term consequences. Without volunteers, the firm may incur insolvency and lose all employment due to large-scale fraud.
The centipede game is a game theory game where two players compete for the more significant part of a growing money stockpile. If a player delivers the cache to their opponent, who takes it, they receive less than if they took the pot.
When one player takes the stockpile, the other gets less, ending the centipede game. Each player knows the game’s total number of rounds.
Game theory affects practically every aspect of life. Game theory applies to personal relationships, purchasing, media, and hobbies since others’ choices affect your day.
Strategy Types in Game Theory
In game theory, players have several main options. Each participant must decide how much risk they are willing to accept to achieve the best result.
The Maximax Strategy
Maximax strategies are hedging-free. Participants are all in or all out; they win big or lose everything. Start-up enterprises launching new items should be considered. Their new product may boost their market cap fiftyfold. However, a disastrous product introduction will bankrupt the firm. The participant is prepared to risk the worst to get the best.
Game theory and maximin strategies choose the best of the worst payouts. The individual has chosen to hedge risk and forfeit full reward to avert adverse outcomes. When facing lawsuits, firms often embrace this method. Companies accept a terrible outcome by settling out of court and avoiding transparency. If the matter went to trial, it might have been worse.
A dominating approach involves a player doing what’s best for the play, regardless of what others do. A corporation may expand into a new market, even if competitors have already entered. Confession is the main tactic in the Prisoner’s Dilemma.
Pure strategy requires the least strategic decision-making since it is a decided option regardless of external influences or others. Imagine playing rock-paper-scissors with one player throwing the same shape each time. The method is pure since this participant’s result is well-defined (specified or not).
Creating a mixed approach may appear haphazard, but it requires careful planning. Consider a baseball pitcher-hitter connection. The pitcher cannot throw the same pitch every time since the hitter may foresee it. The pitcher must change their tactics from pitch to pitch to capitalize on unpredictability.
Game Theory Limitations
Like most economic models, this theory assumes rational, self-interested, and utility-maximizing players, which is its major flaw. Naturally, we cooperate at our own expense as social animals. This theory cannot explain why we may reach a Nash equilibrium dependent on the social setting and participants.
Additionally, game theory struggles to account for human traits like loyalty, honesty, and empathy. Statistics and mathematics can suggest the optimum course of action, but humans may not follow it owing to incalculable and complicated self-sacrifice or manipulative scenarios. Game theory can examine behavior but not predict human behavior.
What Games Does Game Theory Play?
This theory studies the strategic behaviors of two or more “players” in a set-rules, set-outcome environment. Game theory is most commonly applied in business and economics.
Some “games” involve how two competitors will react to price cuts by the other, whether a corporation should buy another, or how stock market traders will react to price changes. Theoretically, these games include prisoner’s dilemmas, dictator games, hawk-and-dove, and Bach/Stravinsky.
Assumptions about these games
Like many economic models, game theory requires stringent assumptions to generate accurate predictions. First, all participants are utility-maximizing rational actors with complete knowledge of the game, rules, and consequences. Players can’t talk or interact. Possible consequences are known and unchangeable. A game can have unlimited participants, but most have two.
Definition of Nash Equilibrium
According to Nash equilibrium, a game is stable when no player may gain an advantage by unilaterally altering a strategy, as long as other players do not change their plans. Nash equilibrium is a non-cooperative (adversarial) game solution. In 1994, John Nash won the Nobel Prize for his work.
Who created game theory?
Developed in the 1940s by mathematician John von Neumann and economist Oskar Morgenstern, game theory continues to be a studied and applied science field today.
This theory examines how competing strategies and player behaviors affect outcomes. Business uses game theory, relevant to war, biology, and many aspects of life, to model strategic relationships in which one firm or product’s outcome depends on others.
- This theory models social settings between competing players.
- The theory aims to optimize independent and competing players’ decisions in strategic settings.
- It may forecast real-world outcomes for pricing rivalry, product debuts, and other events.
- Prisoner’s dilemma, dictator game, and others are scenarios.
- Game theory can be cooperative/non-cooperative, zero-sum/non-zero-sum, or simultaneous/sequential.