Power and changing modes of governance in the euro crisis

Which European Union actors are most powerful in the governance of the euro crisis? The euro crisis has reignited the classic debate between intergovernmentalists, who tend to stress the coercive power of dominant member states in the European Council, and supranationalists, who maintain that through the use of institutional power, the Commission, and the European Central Bank turned out the “ winners ” of the crisis. This article argues that euro crisis governance is best understood not just in terms of one form of power but instead as evolving through different constellations of coercive, institutional, and ideational power that favored different EU actors over the course of the crisis, from the initial fast-burning phase (2010 – 2012), where the coercive and ideational power of Northern European member states in the European Council was strongest, to the slow-burning phase (2012 – 2016), when greater influence was afforded supranational actors through the use of ideational and institutional power.

calculation (Hoffmann, 1966;Moravcsik, 1993;Schimmelfennig, 2015) and the "new" intergovernmentalists who instead highlight member states' search for consensus through discursive deliberation (Bickerton, Hodson, & Puetter, 2015;Puetter, 2012). On the other side are the supranationalists, who argue that bureaucratic or regulatory actors like the Commission and the European Central Bank (ECB) have been able to increase their control over economic governance despite the European Council's efforts to dominate the crisis management process. These encompass the "traditional" supranationalists who emphasize technical actors' use of institutional rules and dynamics Sandholtz & Zysman, 1989) and the "new" supranationalists who focus on such agents' ideas and institutional entrepreneurship (Bauer & Becker, 2014;Dehousse, 2015;Epstein & Rhodes, 2016).
In disagreeing over who has power and how they have gained or lost it, EU scholars generally leave undefined what they mean by power. Taking a conceptual vantage point, the article suggests that the key to assessing the different claims of scholars can be found in their implicit understandings of power. Moreover, the article advances the argument that to account for the changing modes of governance in the euro crisis we need to employ a multidimensional conception of power-as coercive, institutional, and ideational. Although these three dimensions of power are generally relevant for analyzing any political system (Barnett & Duvall, 2005;Lukes, 1974), we would argue that the highly compound governance structure of the European Union (Schmidt, 2006) renders a multidimensional understanding of power-which retains an analytical openness and does not a priori privilege certain actors or institutions-particularly important.
Drawing on approaches to power from the general political science literature as well as from EU studies, Section 2 of this article identifies the three forms of power relevant for analyzing the euro crisis. Building on existing research on the management of the euro crisis, Section 3 demonstrates the usefulness of combining these approaches with power in the analysis of the changing modes of governance in the crisis. The analysis shows, first, that more than one form of power is relevant for understanding how crisis management developed during the crisis and, second, that relations of power changed through the crisis. Succinctly put, in the fast-burning phase (2010)(2011)(2012) of the crisis, intergovernmental actors, notably Germany, took center stage in the European Council and during EU summits, employing coercive and ideational power to frame the crisis as a problem of fiscal profligacy with austerity and structural reform as the only solution. But as the crisis moved to a more slowburning period (2012)(2013)(2014)(2015), supranational actors (notably the Commission and the ECB) exercised greater control and discretion. Increasing economic pressures to save the euro that followed from the adverse consequences of crisis management in the first part of the crisis opened up space for supranational actors to employ ideational and institutional power to leverage their expertise and implementation capacity in ways that challenged the coalition of Northern European member states, which themselves were no longer able to dominate the European Council.
This does not mean that coercive power was no longer important in accounting for the dynamics of the crisis but rather that the relative importance of the three forms of power became more balanced through the crisis, in particular as institutional power and ideational power came to the fore. In other words, although coercive power came to share the stage with institutional and ideational power, it clearly never left the stage. Indeed, as evidenced by recent rounds of brinkmanship and tough bargaining between creditors, the Troika and the Greek government (see Tsebelis, 2015), coercive power remains as central for understanding the changing modes of governance in the euro crisis as do institutional and ideational power.

| THRE E DI ME NS I ONS O F P O W ER
In the euro crisis, a series of questions arise when assessing power and changing modes of governance. Who has had the power to decide what to do in the euro crisis? Which modes of governance have been predominant? What kind of power was exercised-coercive, institutional, or ideational? To answer these questions, we consider the different EU actors and the varying modes of governance in two different periods of the euro crisis. We thus differentiate between fast-and slow-burning phases of the crisis (see Seabrooke & Tsingou, 2016), that is, during 2010 to 2012, when the crisis was "hot" and required quick responses from actors in a position to decide, and from 2012 on, when the crisis continued to burn, but was "colder," allowing more time for reflection on optimal solutions. However, to differentiate between different dimensions of power, and how they mattered for governance during the euro crisis, we require as a starting point a general notion of power. Here, we draw on the later Lukes's (2005) insightful combination of theoretical perspectives that focus on direct decision-making power (Dahl, 1957), indirect agenda-setting power (Bachrach & Baratz, 1970), and preference shaping (Lukes, 1974). Lukes (2005, p. 65) defines power as "agents' abilities to bring about significant effects, specifically by furthering their own interests and/or affecting the interest of others, whether positively or negatively." Taking this definition of power as our starting point has a number of important implications. First, we focus on the capacity to promote or inhibit the interests of actors. In this perspective, power is not equal simply to causality, where power means having some kind of effect on the behavior (broadly conceived) of others. Our definition of power instead focuses on those instances where the actions of A impact the ability of B to get what he, she, or it wants, whether positively or negatively. Second, power is conceived in agency terms. This means that when speaking of power, we are referring to the capacities of (individual or collective) agents to affect the interests of other actors and not to the ways in which economic, political, or ideational structures per se may affect the interests of actors. While such structures may serve as resources in or objects of agents' power relations, they are not at the center of our definition of power, which involves agents with relative autonomy who could have acted differently had power not been exercised. In short, power implies that choices were made that impacted the interests of agents.

| Coercive power
One very common understanding of political power concerns relations of interaction of direct control by one actor over another where these relations allow one actor to shape directly the circumstances or action of another (Barnett & Duvall, 2005, pp. 43, 49)-this is what we here term coercive power. This understanding of power is found for example in the work of the pluralist Dahl (1957), who defined power as instances where "A has power over B to the extent that he [sic] can get B to do something that B would not otherwise do" (pp. 202-203). The approaches to power analysis within the rubric of coercive power generally share certain characteristics, notably to consider power in zero-sum terms, that is, that A's wielding of power entails an equivalent loss of power for B, because the interest of A runs counter to the interest of B; to consider power as a direct causal relation between intentional actors, which in turn excludes power as "action at a distance," that is, without some "connection" between A and B (Dahl, 1957); and to think of the use of power as an action that includes-or threatens to include if orders are not followed-negative sanctions.
In the context of EU scholarship, coercive power is most often related to arguments about who controls the integration process. Thus, the traditional intergovernmentalists-whether realists who assume that member states' positions derive from national interests (Hoffmann, 1966) or liberals who insist that they instead originate in domestic socioeconomic interest-argue that member states delegate power to supranational institutions only to the extent that national governments converge on such an outcome (Moravcsik, 1993), or it helps them to credibly commit to new institutions (Pollack, 2003). In other words, the institutional setup is largely a reflection of the power resources of the member states. Accounts tend to be mainly rationalist, focused on the interest-based hard bargaining taking place between member states (Milward, 1992), with bargaining success dependent on the material resources that actors are willing and able to bring to the table (Keohane & Nye, 1997) and the relative voting weights of member states under various qualified majority voting formulas (Thomson, Stokman, Achen, & K€ onig, 2006). Such arguments place member states as the locus of power in the EU and bargaining among political elites in the European Council as the primary process through which power is practiced. In this view, factors exogenous to the bargaining situation-notably the resources of relevant actors-interact with endogenous factors such as the potential coalitions available, with bargaining between actors being shaped by each player's expectation of what their opponent will accept (Costello & Thomson, 2013).
The exercise of coercive power is not necessarily limited to EU institutional actors. Although EU scholars tend to underemphasize the role of market actors for EU crisis responses-treating them largely as an exogenous factor-they are among the potentially most powerful actors outside national and supranational political systems. To be sure, and as argued below, the actions of bond investors were particularly important in the euro crisis (see also Brunnermeier, James, & Landau, 2016). However, conceiving of the actions of market actors in terms of coercive power is not without its conceptual problems. As laid out above, we think of power in agency terms, as the furthering of actors' interests at the expense of the interests of other actors. It is obvious that markets often significantly impact actors' interests, but it is not always clear that such effects may be traced back to particular actors. In some cases, investors carry so much clout in the market that they are able to exercise direct power over governments and organizations, while in other cases effects occur as a result of more general market developments that may not be connected to specific market actors. Thus, whether we may speak of coercive power with regard to the effects market actors have had in the euro crisis turns crucially on whether such effects have been directly sought by actors or rather are the unforeseen consequences of general market trends.

| Institutional power
A conception of power as coercive is not the only way to consider power. As noted by Costello and Thomson (2013), conceiving of power in terms of decision making through direct interaction between actors within an institutional setting is not useful in all situations relating to the power of EU institutional actors, since power also matters in the agenda-setting and implementation stages of EU policy making. We therefore suggest institutional power as another conception of power that plays a central role in studies of the EU. Institutional power may be defined as actors' control of others through the formal and informal institutions that mediate between A and B (Barnett & Duvall, 2005, p. 51). In this view, institutions are neither neutral coordinating mechanisms nor simply derivatives of coercive power but in fact reflect, and also reproduce and magnify, particular patterns of power distribution (Thelen, 1999, p. 394).
In this institutional perspective, the scope of the parts of the policy-making process taken into consideration is significantly widened to also include the agenda-setting and implementation stages (Bachrach & Baratz, 1970). Including these stages of the policy-making process opens the way for an appreciation of the potential impact of gaps between the control that member states are able to exercise over institutions and the discretion of institutional actors (Pierson, 1996). Such institutional considerations generally serve to pinpoint the sources of power in supranationalism, whether the "traditional" supranationalism, where supranational technical actors' institutional position is at the basis of their agenda-setting empowerment (e.g., Sandholtz & Zysman, 1989), or the "new" constructivist supranationalism, where technical actors set the agenda for intergovernmental political elites through their ideas for policy initiation or about subsequent enforcement (Dehousse, 2015). Alternatively, however, arguments about institutional power could equally be seen to reinforce the position of the "new" intergovernmentalists who contend that the political elites in the European Council have since the Maastricht Treaty recovered their power from supranational institutions by regaining control of the agenda and by creating de novo regulatory bodies rather than adding to the duties of the traditional supranational actors (the Commission in particular; Bickerton et al., 2015).
One drawback to the institutional analysis of power in EU studies is that it is often concerned mainly with the formal institutional attributes of power, such as established position, rules formalized by treaties, or informal rules that become institutionalized regularities, for example, who gets to table a proposal. In this view, institutional power depends on how formal and informal institutional constraints affect political actors' ability to set the agenda and realize their own policy preferences in the face of competing preferences (Thomson, 2015). As already indicated, we suggest a more expansive understanding of institutional power to also include the more concrete interpretation and implementation of rules. Here, we follow the insights of Streeck and Thelen, (2005) that one central driver of gradual institutional change is the continual reinterpretation of what an institution can mean, as new rules may be layered on the old while old rules may be reinterpreted or converted, or allowed to drift. Thus, for example, traditional supranationalists sometimes point to the increasing institutional power of supranational actors through the "redirection" of existing instruments, as in the case of the ECB's new supervisory responsibilities for a banking union; the invention of new rules "copied" from older institutions, as in the case of the European financial stability facility (EFSF); and the "replacement" of institutions, as with the substitution of the EFSF by the European Stability Mechanism (Verdun, 2015, pp. 226-228).

| Ideational power
We define ideational power as the capacity of actors to influence other actors' normative and cognitive beliefs through the use of ideational elements (Carstensen & Schmidt, 2016). This may occur directly through persuasion or imposition or indirectly by influencing the ideational context that defines the range of possibilities of others. This perspective highlights the importance of dominant ideas, in particular with regard to framing the crisis response of both member states and supranational actors, as well as of discourse, especially through the continual need to legitimize policy, which might be problematic institutionally as well as politically if the need for legitimacy is not heeded (Blyth, 2013;Schmidt, 2015). Moreover, this approach is equally open to the possibility that other EU actors, long considered powerless, whether in material or institutional terms, can by dint of their ideas and discourse gain greater power.
Following Carstensen and Schmidt (2016), we differentiate between three forms that ideational power may take-power through ideas, power over ideas, and power in ideas. First, ideational power occurs when actors have the capacity to persuade other actors of the cognitive validity and/or normative value of their worldview through the use of ideational elements (power through ideas). They tend to do this via discourses intended to explain and/or legitimate their proposals and actions, whether in coordination with other policy actors (coordinative discourse), communication with the public (communicative discourse; Schmidt, 2008), or speaking to the markets to convince market actors of the efficiency of proposed solutions (Schmidt, 2014). Examples include the ECB acting as a policy entrepreneur when persuading the Council, and in particular Chancellor Merkel, to agree to Banking Union (Dehousse, 2015;De Rynck, 2016)  Second, ideational power is manifested as a capacity of actors to control and dominate the meaning of ideas, either directly by imposing their ideas or indirectly through shaming opponents into conformity or resisting alternative interpretations (power over ideas). This version of ideational power connects with more coercive forms of power, since here the beliefs of others are directly disregarded. The most obvious example of ideational domination has been from the "Brussels-Frankfurt consensus" (the ECB, the Commission, and Germany, including the Bundesbank; Howarth & Rommerskirchen, 2013). This was most notable in these actors' capacity to frame the crisis for all other EU actors and citizens, like it or not, as one of public debt rather than private, diagnose the crisis as behavioral, as resulting from the failure to follow the rules rather than from the structure of the euro, and, therefore, to prescribe remedies of austerity and structural reform that failed to resolve the crisis (Blyth, 2013;Matthijs & McNamara, 2015). Alternatively, power over ideas can also come from less powerful actors, by shaming their more powerful opponents into agreement. One example of this comes from the "new" parliamentarists' account of how the main parties in the EP successfully pushed the idea of the Spitzenkandidat, in which the leader of the winning majority in the elections would have to be named president of the Commission, despite major resistance from powerful European Council members (notably Germany and the United Kingdom).
Third, and finally, ideational power shows itself when certain ideas enjoy authority in structuring thought or institutionalizing certain ideas at the expense of other ideas (power in ideas). Here ideational power is most closely related to institutional forms of power, since it concerns the ways that historically specific structures of meaning or the institutional setup of a polity or a policy area enhances or diminishes the ability of actors to promote their ideas. This certainly speaks to the ways in which German ordoliberal ideas of the "stability culture" were institutionally embedded in the ECB's Charter, in the Maastricht criteria, and in the Stability and Growth Pact, as well as how EU intergovernmental and supranational actors all found it easiest to agree to reinforce the rules and numbers in the eurozone in the heat of the crisis.

| P OW ER I N TH E F AS T-BUR NI NG EU RO CR I S IS
Since most narratives of the crisis start with member-state action in the European Council in the fastburning phase of the crisis, we too begin here. Such narratives tend to support intergovernmentalist arguments as they depict the member state leaders as the most powerful players in the crisis, meeting ever more frequently in the European Council and in Summits to fight the increasingly hot market winds fanning the flames of the euro crisis, to disagree, delay, bargain, and ultimately act at the last minute, time and again (e.g., Bastasin, 2015). In all of this, the Commission appears relegated to acting as a secretariat. The member states in the European Council saw themselves as the only democratically legitimate actors in the crisis, and the ones called on to act together as they represented their citizens and pledged their nation's financial support to shore up member states in trouble (Schmidt, 2015). Arguments supporting the traditional rationalist intergovernmentalist interpretation of coercive power generally present euro crisis decisions as ones in which government preferences are shaped by national structural financial and economic positions-not party politics (e.g., Schimmelfennig, 2014, pp. 327-328). It is striking how much of the focus has been on how the economic strength of certain member states has given them the coercive power to impose the costs of adjustment on the economically weaker member states suffering the most from the crisis, to the great detriment of the latter. Most commentators see a divide between a coalition of highly solvent "creditor" countries, led by Germany (and including Finland, Austria, and the Netherlands), which benefit from moderate sovereign debt, market confidence, and low interest rates on sovereign debt, versus a coalition of highly indebted or deficit-ridden countries, led by France (and including Southern European countries) suffering from high interest rates on sovereign debt and low market confidence (Schimmelfennig, 2015). In these power relations, the Northern Europeans had the upper hand over the Southern Europeans, and Germany in particular over France. As the traditional Franco-German "couple" that used to serve as leader of the EU reduced itself to German leadership because of France's loss of economic credibility, France took a progressively more active role in leading the coalition of Southern European countries (Vail, 2015).
Central to these arguments stands the coercive power of Germany, based in large part on the economic strength of the German economy and its status as primary creditor in the setting up of loan programs and crisis management mechanisms, making it the sine qua non of decision making in the European Council (Matthijs, 2016b;Thompson, 2015). Such coercive power of Germany in the fastburning phase of the euro crisis was further bolstered by the ideational power of the Northern European coalition to impose their own ideas over all others about what to do-that is, through the reinforcement of the "stability" rules of the Stability and Growth Pact-as well as to resist ideas proposing institutional innovation in the European Monetary Union (EMU), such as Eurobonds or a European Monetary Fund. More specifically, German leadership has consistently been described as able to impose its own ideas about the crisis and what to do while resisting any alternative ideas. France, in contrast, has increasingly lost its power to impose its own ideas (Vail, 2015). Consider the difference between Sarkozy from 2008 to 2010, when he appeared to be the leader of the neo-Keynesian crisis response, and from 2010 to 2012, when he became the junior partner in the bilateral directoire of "Merkozy," and slowly but surely gave up his discourse of solidarity for one focused on stability (Crespy & Schmidt, 2014).
Here, coercive and ideational power combined enabled the Northern European member-state coalition to effectively keep out alternative policy ideas. Notably, it was primarily Germany, supported by its coalitional allies, together with the ECB and the Commission, that framed the crisis as one of public debt rather than the socializing of private debt resulting from the overindebtedness of the banks and households (Blyth, 2013). It was also Germany that defined the problems as behavioral, from member states not following the rules, rather than resulting from the structure of the euro, as most economists argue (De Grauwe, 2013). Likewise, it was Germany that rejected in no uncertain terms any deep solutions, such as Eurobonds, and resisted even a banking union for a very long time. Thus, Merkel made good on her pledge to the German public that: "I will take care that we make sure together with our partners that the whole of Europe commits herself to 'a new Stability Culture'" (cited in Howarth & Rommerskirchen, 2013, p. 762).
At the same time that this was about Germany's power over ideas, however, we could also make the case that this was about power in ideas. After all, it was Germany's long-standing ordoliberal philosophy about how to run an economy that infused the ECB's view of its mandate (imported from the Bundesbank; Blyth, 2013). Moreover, these are the ideas that informed the "Brussels-Frankfurt consensus" on austerity and structural reform (Jones, 2015). And they were also the ideas that infused the European Parliament and guided its actions in the exercise of what little institutional power it had at the onset of the eurozone crisis. The heightened sense of crisis combined with the conviction that there was no alternative to ordoliberal austerity was such that most MEPs voted for reinforcing the rules in the Six-Pack and the Two-Pack-indeed, pushed for more stringent measures than were on the table (i.e., by adding reverse qualified majority voting which effectively limited the European Council's institutional power to block Commission sanctions).
One may object that the ideational power of Northern European "creditor countries" to impose their ideas about crisis management and structural reform was of limited importance, since their discourses did little in way of winning the hearts and minds of elites, let alone publics, in "debtor countries." In this view, coercive power was the real driver of bargaining and reform processes. To be sure, the exercise of coercive power was essential for the efforts of German leaders and other Northern European members of the euro to push through their policies and reform demands, but one should not discount the importance that the power over elite and public debates had for the effectiveness with which coercive power was exercised. Thus, power is most effectively exercised when it is accepted following its justifiability in terms of the beliefs and norms held by subordinates (Beetham, 1991), which makes ideational power a key part of the effective exercise of coercive power. The capacity of policy actors to dominate debates about the diagnosis of what the crisis was about and what treatment would be most effective was crucial not only for persuading the elites and the electorate in "creditor countries" about the right way forward (and, crucially, who should lead the way forward), but also for setting the tone of debate in the countries most hurt by the crisis. Clearly it would be a step too far to claim that elites and publics in "debtor countries" simply accepted the exercise of coercive power on the part of Northern European "creditor countries." However, as shown by Kriesi and Grande's (2014) analysis of public debates about euro crisis management, German leadership and supranational actors, along with their economic rather than cultural frames on the crisis, were very well represented across the EU member states. The majority of elites and the electorate in Southern European member states might not have agreed with the German approach, but the efforts of actors in "creditor countries" to exercise ideational power was effective to the extent that their frames came to dominate public debate about the euro zone crisis, in turn buttressing the preferred crisis management approach of Northern European euro zone member states.
It is also worth noting that despite the leadership role of Germany in the management of the euro crisis, German power was, as granted by even staunch supporters of intergovernmental scholarship, never absolute. If Germany is the "hegemon" rationally calculating its interests and imposing its ideas in the eurozone crisis, it has been a highly unsuccessful one at that. Germany has been, rather, a "reluctant" hegemon (Bulmer & Patterson, 2014) that has not wanted to lead and suffered the consequences. A number of analysts point to the miscalculations of German leaders, whose reluctance to bail out Greece early in the crisis meant that the crisis spiraled rapidly almost out of control-making any bailout much more costly-before Chancellor Merkel finally agreed very reluctantly to the May 2010 actions. These included the loan bailout for Greece and the EFSF as a bailout funding mechanism for other countries under threat of attack from the markets as a result of contagion from the Greek crisis (Bastasin, 2015). And all of this went against Germany's initial calculation of its interests or ideas about what should be done (Matthijs, 2016a).
The ECB clearly also played a central role in the fast-burning phase of the euro crisis. Central banks in advanced industrialized countries have over the years become increasingly insulated from politics, and the ECB is the example of this par excellence. It has autonomy with little democratic control from the classic "democratic circuit" of parliamentary oversight (H eritier & Lehmkuhl, 2011, pp. 138-139), leading to a high degree of institutional power in implementing its policies. The ECB thus has the autonomy to reinterpret the rules set out in its Charter so long as it can gain agreement internally from the member states sitting on its governing board. Initially, the ECB sought to manage perceptions with a communicative discourse emphasizing the importance of maintaining its "credibility" through strict adherence to its rules of inflation fighting while resisting any political pressure from member-state leaders. Under the helm of governor Jean-Claude Trichet, this insistence on sticking to the standard interpretation of its mandate translated into a modest nonstandard bond-buying program, in particular compared to the Federal Reserve or the Bank of England. Despite the modesty of these programs, the ECB still leveraged the coercive power that followed from its monetary resources and strong independence to press member states to engage in austerity and structural reform in a quid pro quo for its own more vigorous monetary interventions (Schmidt, 2015).
Most initial narratives of the crisis took at face value the intergovernmental story of political leaders' agenda-setting role throughout the crisis, mainly because they paid attention to the players at the front of the stage. The new intergovernmentalists in particular noted that the Commission was "not very visible in early crisis management" (Puetter, 2012, p. 172) and appeared "indecisive and uninspiring" thereafter (Menz & Smith, 2013, p. 202). But over time, new narratives have added supranational stories, focused in particular on EU technical actors not only in the ECB but also in the Commission as occupying a greater place in formulating, implementing, and evaluating policy (Bauer & Becker, 2014, pp. 214-215). Compared to the ECB, the Commission has less margin for maneuver, since the rules it devises and administers have been decided by the European Council (with the EP in certain instances) and pushed by the ECB. That said, within the context of the rules agreed by the European Council, the Commission does have room for manoeuver with regard to its (re)interpretation of the rules (Schmidt, 2016).
Despite not being privileged with as great institutional power as the ECB, it is worth noting that even in the fast-burning part of the crisis, and despite having lost its agenda-setting powers of the Community Method, the Commission has exerted ideational power in the earlier parts of the crisis. As new supranationalists have argued (e.g., Bauer & Becker, 2014;Dehousse, 2015;Epstein & Rhodes, 2016), EU technical actors had been playing major roles throughout by providing the intergovernmental political actors with new ideas for the policy initiatives, some of which had been worked out long before. So the supranational story is not only about the exercise of institutional power (see below) but also about the ideational power through ideas that supranational actors have exercised as they developed and proposed to the intergovernmental political leaders the policy initiatives they then later came to enforce.
The European Semester, for example, which has given the Commission unprecedented oversight authority and enforcement powers with regard to member-state governments' budgets, was long in coming. The Commission, acting like a stubborn ideational policy entrepreneur over a long period of time, developed the idea in deliberation with think tanks and expert consultants, commissioned reports on it, inserted it as blueprints in the European Council's political debates and in legislative proposals, and saw it finally come to fruition when the crisis served as the propitious "window of opportunity" (Dehousse, 2015). Similarly, Banking Union, prepared by the ECB in consultation with experts and discussed with political leaders-in particular Chancellor Merkel in a charm offensive by ECB President Draghi over a period of a year (Spiegel, 2014)-has given the ECB unprecedented supervisory authority and resolution powers over member-state banks (Dehousse, 2015;Schmidt, 2016). In other words, despite the dominance of member states in the initial fast-burning phase of the crisis, EU supranational actors have been active policy entrepreneurs, generating the ideas for the policies that subsequently empower them to more proactively shape the reform agenda of the euro crisis.

| P OW ER I N TH E S LOW -BURN IN G EUR O CRI S I S
As the crisis moved from fast burning to slow burning, the ECB and the Commission, which had remained at the back of the stage, moved forward, to be seen also as key actors in the pageant. This was due in part to the new institutional powers of oversight and enforcement gained as a result of intergovernmental action. Thus, the traditional supranationalism of leadership by the technical actors in the Commission may have indeed diminished, much as the new intergovernmentalists argue, but in its place, supranational actors-whether in the Commission, the ECB, or de novo bodies-have gained even greater institutional powers of enforcement than in the past, and this through the very rules passed by the more active (new) intergovernmental political leaders.
To see how the shift toward increased power for supranational actors occurred, it is helpful to once again start with the intergovernmental level and Germany's coercive power in the European Council. The switch from the fast-burning to the slow-burning phase of the crisis signaled not only an increased role for supranational actors, but also an increasing recognition-more often borne out in actions than in discourse-that the ordoliberal ideas that had framed policy making in the initial phase of the crisis, along with German foot-dragging that time and again frightened bond markets, was causing more damage than providing viable solutions to bring the EMU on a firmer footing. Until the summer of 2012, Germany stuck to a narrow version of its ordoliberal ideas, despite evidence that the resulting policies were systematically doing damage in material terms (Matthijs, 2016a). However, by 2012, it was clear from the slowing of the European economy as a whole that the rules were not working as anticipated, and the consensus-seeking deliberation in the European Council turned to greater contestation, as Italian and French leaders in particular sought to exert power through ideas to persuade other member-state leaders, and in particular German leaders, to change course. Growth entered the European Council's discourse already in late 2011, pushed by the Italian Prime Minister Monti and then Hollande, first as presidential candidate and then French president, to be taken up by Merkel, who agreed to stability and growth by mid-2012. These shifts in discourse came to have significant influence on the management of the subsequent slow-burning crisis. Similarly, flexibility entered the European Council's discourse in 2014, brought by the new Italian Prime Minister Renzi, and supported by Hollande, and after some contestation pushing Merkel to agree to flexibility "within the stability rules." Although this did not necessarily alter the European Council's actions, it did make a difference for the Commission in the European Semester beginning in 2012, which adopted a new focus on growth, and beginning in 2014 and even more in 2015, with an emphasis on flexible reinterpretation of the rules (Schmidt, 2015).
Another prominent example of reinterpreting the rules-which involved a mix of institutional power through incremental rules change and ideational power through ideas-is the shift in the ECB's approach from the earlier fast-burning phase to the slow-burning phase. When first appointed head of the ECB in late 2011, Trichet's successor Mario Draghi initially continued with the discourse of "credibility" while denying that the ECB could be a lender of last resort. But by spring 2012, as the ECB engaged in more robust bond-buying programs, he switched his legitimizing discourse to a focus on "stability." The switch from the credibility discourse also opened space for the ECB to engage in informal interactions with EU leaders in the European Council. Unlike Trichet, Draghi sought to coordinate with European Council leaders, including his year-long "charm offensive" to persuade Chancellor Merkel in particular that "unorthodox" bond-buying programs and a banking union were essential. All the while, the ECB was working to fashion policy packages acceptable (to Germany) and workable (for EMU) in the face of Bundesbank scepticism. Draghi succeeded in getting around Bundesbank opposition largely via Merkel and after bypassing the objections of the German representatives on the ECB board (Schmidt, 2016). But while the ECB switched its discourse from credibility to stability beginning in 2011, it continued to deny publicly that it would or could act as a lender of last resort for member states despite slowly and incrementally layering on increasingly "unorthodox" bond-buying policy that brought it close to one (Buiter & Rahbari, 2012). The discourse of denial kept the markets worried and primed for panic and attack (Blyth, 2013). Only in July 2012, when Draghi pledged to do "whatever it takes to preserve the euro," did the markets stop their massive attacks against Spanish and Italian sovereign debt.
So how do we explain the ECB's remarkable reversals, in particular given the continual denials in the discourse? In terms of ideas, we could explain the ECB's slow, incremental shifts as a search for solutions in which its precrisis "paradigm" did not cover all contingencies. As a result, the ECB had to engage in a continual process of "bricolage" (Carstensen, 2011) through which it introduced increasingly "unorthodox" policies that were unimagined prior to the crisis. These were the ad hoc responses of the ECB agents using their ideational power to puzzle their way through a crisis rather than the result of "willful actors" using their coercive power to seize the moment (Braun, 2013). To explain this in terms of the ECB's ideational power through ideas, we would need to look into the coordinative discourse inside the ECB, as member state representatives of the ECB governing board were engaged behind closed doors in processes of persuasion and contestation. We could even argue that initially the more orthodox central bankers mainly from Northern Europe used their coercive power to form a blocking coalition around Germany, but this changed as more and more Northern European countries rallied around the ECB president, whose power through ideas persuaded them to leave the Bundesbank increasingly on its own to espouse the most orthodox positions (Schmidt, 2016). Ideational entrepreneurship through ideas was thus an added factor in the explanation of the ECB's changing ideas and discourse over time.
The switch in presidents of the ECB was of equally great significance. Trichet was the French statetrained civil servant whose career was focused on institution building in financial and monetary affairs, and whose economic ideas about what to do remained "orthodox." Draghi was much more innovative, having had a more diverse background, and he was a bridge builder (Basham & Roland, 2014). In the progressive reinterpretation of the rules to "save the euro," not only did Draghi manage to bring fellow central bankers on board, he was also able to exercise his persuasive ideational power with European Council leaders, developing sufficient rapport with European Council leaders-and in particular Chancellor Markel-so as to gain their trust and support as well (Bastasin, 2015). However, even as Draghi managed to implement more comprehensive monetary programs, strong conditionality still played an important role in the setup of the Outright Monetary Transaction program, probably to satisfy opposing political forces within the Governing Council (Lombardi & Moschella, 2016). This serves as a reminder that the particular institutional setup of the ECB-with power placed in the Governing Board made up of 19 central bank governors of the euro area countries, and 6 members appointed by the EU-limits the power of the governor and makes the capacity to establish coalitions paramount.
More generally, the ECB itself has been very successful as an ideational policy entrepreneur overall. In a banking union, for example, a dominant group in the ECB in 2012 took advantage of European Council decision makers' high uncertainty, teamed up with the Commission (Epstein & Rhodes, 2016) and employed power through ideas-specifically by combining the notion of a "vicious circle" between banks and the sovereigns and the long-standing idea of centralizing banking supervision in the ECB-to help preferences converge around the idea of giving up national supervisory powers (De Rynck, 2016). Notably, the outcome went against German interests, suggesting that by reframing the problem, policy entrepreneurs were able to effectively employ ideational power, in turn trumping the coercive power of the Northern European coalition (see Schäfer, 2016).
Other supranational actors were equally able to use both institutional and ideational power in influencing the reform process in the slow-burning phase of the crisis. Notably, the Commission also had significant institutional powers, both to propose rules and, once passed, to bend them to its purposes. In rationalist terms, we could explain the Commission's powers by the fact that with so many principals holding different views in the intergovernmental Council, the Commission as its delegated agent could enjoy a high degree of discretion (Dehousse, 2015, p. 11). In institutional terms, the Commission's powers of discretion are most apparent in the increasing flexibility it has exercised in its interpretation of the rules over time, as it layered new elements onto the old, reinterpreted the rules, or even converted them. But unlike the ECB, which has the autonomy to reinterpret its own rules, and therefore communicated that its reinterpretations remain true to its cardinal rules, the Commission largely sought to hide its increasing flexibility with a continued harsh discourse focused on pushing austerity and structural reforms (Schmidt, 2016). But this suggests that another explanation of its institutional powers of discretion lie in its ideational powers through ideas, and a discourse that sought to persuade that it actually was not exercising that discretion.
In the absence of real remedies to the crisis, such as a fiscal union or eurobonds, the Commission was stuck with searching for solutions "like the drunk who looks for his lost keys under the lamp post" because "that's where the light is" (Mabbett & Schelkle, 2014). Recognizing this reality, in particular as performance deteriorated, the Commission began altering the procedures, by making exceptions and flexible adjustments for nonprogram countries, such as derogations of the rules for individual member states (e.g., extending the time for France and Italy to bring their deficits under the target numbers) or recalibrating the calculations (e.g., for Spain on the structural deficit), even as it denied publicly any leniency so as to circumvent objections from pro-austerity European Council members (Bauer & Becker, 2014;Schmidt, 2016). In so doing, the Commission sought to forestall problems with the markets, which it assumed wanted such policies; to avoid conflict with the European Council, given the internal political divisions; and to ensure against any possible legal action.
Only with the inception of a new Commission in November 2014 have the practices and the discourse seemed to be coming into greater alignment. The Juncker Commission began exercising more autonomous institutional power along with greater ideational power through persuasion, as it presented structural reform as a quid quo pro for greater flexibility through slower deficit reduction (with France and Italy given yet another 2-year extension on deficit reduction on these grounds). It also pledged to do more to alleviate the social costs of the crisis, as well as to promote growth through an investment fund. Moreover, the Commission's new double accountability-not just with the European Council but as of 2015 also with the EP as a result of the appointment of the leader of the winning majority in EP elections (the Spitzenkandidat) as Commission President-may give it the needed independence from the European Council to be more truly innovative-and powerful both ideationally and institutionally-during the continuing slow-burning crisis phase.

| CONC LUS I ON
To conclude, we may once again ask which institutional actor has been in the driver's seat during the euro crisis. As shown above, it is not possible to point to one institutional actor that has won more power during the euro crisis. That should not be taken as a sign that power is somehow not important in the crisis. Different institutional actors did indeed exercise power-whether in the form of coercive, institutional, or ideational power-or, as often was the case, a combination of all three forms of power. The analysis thus demonstrates the two basic claims of the article, namely that it is not possible to point to either one institutional actor or one form of power in accounting for the crisis, and that the relative power of different institutional actors changed throughout the fast-or slow-burning phase of the euro crisis. The analysis shows that during the fast-burning phase of the Eurozone crisis, intergovernmental actors dominated by Germany exercised greater power, in terms of both rationalist power of coercion and ideational power over ideas, than supranational actors, who nonetheless exercised important institutional and ideational powers through ideas. In contrast, the analysis demonstrates that during the slow-burning phase of the crisis, supranational actors such as the ECB and the Commission exercised equally important if not greater power, mainly in terms of their institutional and ideational powers through ideas, than intergovernmental actors, who at the same time shifted toward more ideational power through ideas while exercising less coercive power.
Analyzing the euro crisis in terms of different and at times competing dimensions of power may push the current debates on who are the main drivers of integration in the EU toward greater appreciation of how the roles of institutional actors have shifted-and not necessarily either diminished or won out-over the course of the crisis. We would thus tend to agree with "new" intergovernmentalists that member states remain very much at the helm of short-term crisis management and longterm reform. However, instead of therefore focusing solely on the power relations between member states, and rather than seeing supranational actors as playing only the role of credible commitment, as second fiddle to powerful member states in the European Council, a multidimensional power approach favors a broader perspective. For supranational actors, it shows that they have not only reinterpreted their role and interest in the integration process, they have also found new avenues for doing so. As a result, supranationalists are right to point to an important entrepreneurial role for the Commission that shifts its major point of influence from the agenda-setting role in the Community Method toward a role of expert implementer of economic governance reforms and provider of new ideas and interpretations, as policies move from the grander perspective of the European Council to the concrete implementation on the ground. In sum, the shifting of EU modes of governance in the eurozone crisis does not represent the pinnacle of member-state power at the expense of supranational or parliamentary actors but, rather, as the Eurozone moves toward greater integration, an increasing mutual dependence between EU institutional actors with different resources that each may bring to the table.
Analyzing the management of the euro crisis from the vantage point of a multidimensional conceptualization of power follows an additive approach to theory building (Jupille, Caporaso, & Checkel, 2003), in the sense that it builds on and combines theories that vary in terms of explanatory factors but share an overall explanatory focus (in this case, the euro crisis; Ioannou, Leblond, & Niemann, 2015). However, rather than identifying the respective "home domains" of the central integration theories in EU studies with the ambition to bring them together in some larger picture, or incorporating them in the "mosaic of integration theory" (Wiener & Diez, 2009), we instead more specifically focus on how different approaches to power may help us understand the management of the euro crisis and the creation of new modes of governance in the EU. That is, to analyze the complexities of the euro crisis, we dispense with ambitions about building grand theory or maximizing parsimony characteristic of decades of unending battles in EU studies. Likewise, we deny integration theories of a private kingdom in the form of designated explanatory "home turfs." Instead, we suggest that political science analyses of crisis management in the euro zone may benefit from a multidimensional power perspective that does not a priori privilege certain sets of actors or certain relations of power, but instead entertains an analytical openness toward which forms of power mattered, and how these forms of power interacted under the relevant temporal and institutional circumstances.


Discussion of “The power of monitoring: how to make the most of a contaminated multivariate sample”

We contribute to the discussion of an article where Andrea Cerioli, Marco Riani, Anthony Atkinson and Aldo Corbellini review the advantages of analyzing multivariate data by monitoring how the estimated model parameters change as the estimation parameters vary. The focus is on robust methods and their sensitivity to the nominal efficiency and breakdown point. In congratulating with the authors for the clear and stimulating exposition, we contribute to its discussion with an overview of what we experienced in applying the monitoring in our application domain.

applications of the monitoring approach to datasets relevant for international trade analysis and anti-fraud, which bring new statistical challenges not yet fully addressed.

Monitoring trade data
CRAC have introduced us to a particular monitoring instance, the Forward Search (FS, Atkinson and Riani 2000), more than ten years ago. We studied together the application of monitoring to other established robust regression estimators (Riani et al. 2014). Currently, we use different forms of monitoring in the routine analysis of large amounts of regression datasets relevant to European Union policies, such as international trade and anti-fraud. We have many more reasons for supporting enthusiastically the approach than drawbacks to signal.
We compute on a monthly basis robust estimates of "fair prices" for goods imported in the European Union from third countries. The estimates are used by customs and anti-fraud services to combat illegal practices. The financial impact for the budget of the EU is very big and the fair prices must be somehow "certified", in view of their use in Court cases. We are therefore studying appropriate statistics or indicators to summarize the sensitivity of the robust fair price estimate to the choice of the estimation method and the related parameters and tuning constants. To this end the monitoring is a precious instrument, although we are facing with two main disadvantages: one is the substantial computation time (which increases with the sample size and number of parameters monitored) and the other is the lack of clear instruments to summarize automatically in a unique statistic or indicator the rich collection of monitored results.
We illustrate the need of monitoring the stability of the fair price estimates, even for small datasets, in Fig. 1, which has to do with imports of "sports footwear with insoles of a length of less than 24 cm". We see the results obtained with the SAS PROC ROBUSTREG and the MATLAB FSDA Toolbox (Riani et al. 2012(Riani et al. , 2015 with four methods: FS, LTS, S and MM. We could verify that the reason for the discordance between the two sets of results originates from the different default parameter values adopted by the two environments. The figure also reports in the caption the FS estimate, which is in line with the results obtained by the other estimators with the FSDA defaults. The typical forward plot associated to the FS (in the top-right panel) shows a sharp decrease of the statistic monitored (the minimum deletion residual), which is sign of structure in the data that the other methods have not addressed properly because of the unlikely choice of the key parameters that determine their robustness and efficiency.

The effect of concentrated non-contaminated observations
We introduce in the discussion another complication that occurs rather often in trade data, consisting in large proportions of non-contaminated observations falling in a small data region. To our knowledge, this problem was addressed in robust statistics only recently, with Heikkonen et al. (2013) and Cerioli and Perrotta (2014) showing that the effect of a high-density region can be so strong to override the benefits of robust devices such as trimming methods for robust clustering. We show that the monitoring plots do not make exception and become completely uninformative in  presence of highly concentrated data. The proposal of Cerioli and Perrotta (2014) in these cases, is to sample a much smaller subset of observations which preserves the cluster structure and also retains the main outliers of the original data set. This goal is achieved by defining the retention probability of each point as an inverse function of the estimated density function for the whole data set. Consider for example the datasets of Fig. 2, which for the sake of clarity will be called respectively "Books" and "Jewellery" datasets. They are both characterized by a densely populated area in a "small trade" region of no practical interest in the anti-fraud context. In the case of the Books dataset, units are so concentrated that only 0.02% of the data is retained, while the general data pattern is preserved. Note that the initial size of these datasets can be so large to make analyses computationally very demanding (the application of the FS to the 33304 books import flows went out of memory after running several hours on a 2.1 GHz Xeon processor with 16 Gb of memory).
To illustrate the issues that we encounter in monitoring this type of datasets, we use first a trade-like dataset simulated for a separate assessment exercise, still in progress. It is represented in Fig. 3 before and after thinning (left and right panel rspectively). Along the lines of CRAC, we monitor the S and MM estimators fit on the original data. To be more general than in the case illustrated in Section 2, from now on we will use a model with intercept. The forward plot trajectories appear as uninformative flat lines, shown in Fig. 4 for the MM estimator.
After thinning, when the same monitoring is applied on the retained units, the forward plots of the S estimator (right panel of Fig. 5) show that, when the breakdown point is chosen between 0.5 and 0.45 the outliers are very well identifiable. On the  values are chosen, with residual trajectories which become closer and closer. After the thinning step, the monitoring on the retained data clearly shows the presence of structure in the data. In the right panel of Fig. 7 a drastic decrease of the residuals occurs below a certain breakdown value, around 10%, suggesting that masking is occurring when the outliers present, which indeed are roughly 10% (about 70 high price outliers among a total of 723 units), start distorting the estimates. In the right panel of Fig. 8 the sudden decrease corresponding to a breakdown point of 0.45 indicates the presence of two major groups in the data.
Note, in both figures, the different scales of the monitored residuals in the original and thinned datasets. To understand the nature of this effect we have monitored the intercept and slope values estimated in the two cases. Figure 9, which refers to the Books dataset, shows that the intercept is close to 0 if all data are fit, while with the retained units it is between 100 and 350, depending on the breakdown point, with Monitoring of the S-regression parameters fit on the Books data, before and after thinning (red and blue line respectively) obvious inflation effect on the residuals. The corresponding slopes for a standard 0.5 breakdown point are respectively around 3.5 and 2.7. We could verify that the most reasonable slope (obtained with a robust fit using a model without intercept, to estimate the import price of the books) is 2.8, which is very close to the S fit on the retained units. Finally note that also the monitoring of the estimated regression parameters shows that something is occurring for a breakdown point approximately equal to 0.1. The monitoring of the minimum deletion residuals with the FS provides similar information about the two trade datasets. The left panel of Fig. 10 clearly shows that the Books dataset is formed by one main population and a set of outliers. The right panel of the same figure, which report the same monitoring (from step 200) for many random starts on the Jewellery dataset, shows different sets of trajectories indicating the presence of multiple groups.

Closure
For CRAC, the monitoring is more than a particular way of dealing with data: they often like to state that it is a truly data analysis philosophy, which comes from the belief that data can be completely understood only by appraising the effect on a fitted model of each statistical unit, or sub-groups of units. In this discussion we have provided other evidence that the monitoring is, at least, a very powerful instrument to summarize lot of information in one single plot.
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.


extfieldsofstudy:
Computer Science
Mathematics

text:
Stability of Leaderless Resource Consumption Networks

In this paper, we study the global stability properties of a multi-agent model of natural resource consumption that balances ecological and social network components in determining the consumption behavior of a group of agents. The social network is assumed to be leaderless, a condition that ensures that no single node has a greater influence than any other node on the dynamics of the resource consumption. It is shown that any network structure can be made leaderless by the social preferences of the agents. The ecological network component includes a quantification of each agent's environmental concern, which captures each individual agent's threshold for when a resource becomes scarce. We show that leaderlessness and a mild bound on agents' environmental concern are jointly sufficient for global asymptotic stability of the consumption network to a positive consumption value, indicating that appropriately configured networks can continuously consume a resource without driving its value to zero. The behavior of these leaderless resource consumption networks is verified in simulation.

I. INTRODUCTION
In the face of an ever-changing natural climate, understanding the behavior of renewable natural resources and the impact of human consumption on those resources is important for ensuring long term resource consumption [1], [2]. Modeling of natural resources allows the prediction of consumption behavior and offers valuable insights into the relationship between various system components. In this paper we study network structure and resource consumption. Of particular interest is the equilibrium behavior of these models, as equilibria can help describe the long term sustainability of natural resources [3]. The discussion of long term system behavior must be preceded by an understanding of the stability properties of the system. This paper focuses on the study of an agent-based model of natural resource consumption previously introduced and studied in [4]- [6]. This model captures insights from the social sciences on the consumption behavior of humans in a form that can be analyzed mathematically. Past work on this model has sought to understand the behavior of the model and has considered stability of this model in the two agent case. This paper extends the consideration of stability to consider n agents interacting over a network.
The overall system consists of an ecological sub-model, which describes the dynamics of the resource, and a social sub-model, describing the dynamics of the agents' consumption. The ecological sub-model is based on the Gordon Schaefer model, which represents a class of well studied systems associated with dynamic processes in population biology, ecological economics and other related disciplines [7], [8]. The stability of the Gordon-Schaefer model, as well as similar logistic growth models, has been studied extensively in isolation from the social processes which drive human consumption behavior [9]- [12].
The social component of the model describes the cognitive decision making process of the agents regarding change in their consumption. This process is influenced both by the state of the resource and the consumption of other neighboring agents. The influence of the agents on each others' consumption is similar to how agents influence each other in mathematical models of opinion formation [13] and consensus in cooperative multi-agent systems [14]. The dependence of the agents' resource consumption on the state of the resource appears as an exogenous factor or time-varying bias in the overall dynamics (see [15], [16] for similar models). An important component of the social process is the underlying social network structure, which greatly influences the ability of a community to successfully manage its natural resources [17], [18]. This paper studies the behavior of a consumption network under the assumption that it is leaderless: that one agent will not drive the social network component of the model more than any other agent in the network. This assumption allows an aggregation of individual state nodes [5], facilitating an understanding of the system-level behavior. Discussing a consuming population in aggregate is a common tool for the study of resource consumer social networks [19] and allows for the design of actions taken to change behavior, which often happen at the community level [18]. The leaderless assumption, as will be shown, also captures a wide array of systems and a rich class of stable system behaviors.
The rest of the paper is organized as follows. Section II introduces the consumption model and discusses its properties. Section III discusses the leaderless condition and presents a Lyapunov based proof for global stability of the system. In Section IV the behavior of leaderless systems is studied in simulation, with a discussion in Section V. The paper concludes in Section VI.

II. SYSTEM DYNAMICS
This section presents the dynamics governing the resource quantity and consumer behavior in the coupled socio-ecological system. We first discuss each sub-model and then give an aggregate leaderless consumption model.

A. The Ecological Sub-model
The ecological component of the system is assumed to consist of a single renewable resource with quantity at time τ represented by R(τ ). In the absence of consumption, the resource grows at intrinsic growth rate r and saturates at carrying capacity R max . The resource is connected to a consuming population consisting of n individuals. Each individual can harvest the resource by exerting consumption effort e i (τ ), where i ∈ {1, . . . , n} represents a single consumer. The resource dynamics are assumed to follow the standard Gordon-Schaefer model [8] with catch coefficient equal to one, which is given as

B. The Social Sub-model
The social sub-model is based on Festinger's theory of social comparison processes [20], which postulates that human beings evaluate their decisions, opinions and abilities by reflecting on both objective and social information. In the context of natural resource consumption, objective information corresponds to the state of the resource and social information corresponds to the consumption of other socially connected individuals [21]. To balance between objective and social information, the change in consumption effort of the agent is given as a weighted sum of both ecological and social factors.
The ecological factor for consumer i is given by R(τ )−R i , where R i ∈ R represents the perceived scarcity threshold of i, below which agent i considers the resource to be scarce, and above which she considers it to be abundant. The ecological factor is weighed by a i ∈ (0, ∞), which represents the set of factors to which agent i attributes the state of the natural resource. An ecological attribution a i → 0 represents a consumer that attributes the state of the resource entirely to the actions of the consuming society (including the agent itself), while increasing values of a i correspond to the individual attributing the current state of the resource to natural causes (droughts, wildfires, heavy rain, etc).
The ecological factor is balanced by a social component, given by , which is the difference between i's consumption and that of the other socially connected consumers in the population. The graph connectivity is captured by ω ij ≥ 0 which is the strength of the social tie directed from j to i. We assume that n j=1 ω ij = 1 and The social factor is weighed by s i ∈ (0, ∞), the social-value orientation of i. Social-value orientations s i → 0 represent extremely non-cooperative individuals, which will ignore the actions of their network neighbors. Conversely, increasing values of s i correspond to increasingly cooperative individuals.
Combining the social and ecological component gives the dynamics of the consumption effort for consumer i as where the ecological and social factors have been weighed in accordance with findings in social psychological research on consumer behavior [4]. In particular, individuals that attribute blame to natural causes tend to give more importance to ecological information and vice versa. Similarly, cooperative individuals are more concerned with maximizing equality in consumption than non-cooperative ones, and as such will be further influenced by the social factor (see [4] and included references for more details).

C. Non-dimensionalized Socio-Ecological System
In order to reduce the dimensionality of the parameter space, the system given by Eq. (1) and (2) is nondimensionalized. The process of non-dimensionalization has an added benefit of allowing comparison between system parameters. The dynamics of the non-dimensionalized state of the resource x = R(τ ) R max and the non-dimensionalized consumption y i = e i r are given as followṡ where i ∈ {1, . . . , n}, and the derivativesẋ andẏ i are taken with respect to the non-dimensional time t = rτ . The non-dimensionalized The parameter b i is the sensitivity of i, which represents i s openness to change in her consumption. The final parameter, ν i , is called the socio-ecological relevance of i and represents the importance that i gives to social information relative to ecological information in the process of changing consumption behavior.

D. Influence and Leadership
The consumption of i is influenced by the consumption of all other agents that are socially connected to her. This notion of connectivity is captured in Eq. (3) via the parameters ω ij , which denote the strength of the social tie directed from j to i. If ω ij = 0 this implies that there is no social link from j to i, allowing the collection of ω ij 's to specify the topology of the underlying social network. The aggregate influence of the rest of the agents on i's consumption is given by n j=1 b i ν i ω ij and is called the in-influence of i. The aggregate influence that i exerts on the other agents in the network is given by n j=1 b j ν j ω ji and is called the out-influence of i. The difference between the out-influence and the in-influence is called the net-influence of i and determines the role of i in the network as a leader (positive net-influence), a follower (negative net-influence) or neutral (zero net-influence). In this paper, we consider cases in which all agents in the network are neutral.
III. GLOBAL ASYMPTOTIC STABILITY OF LEADERLESS NETWORKS In this section, two assumptions on the network and parameters are introduced before transforming the nondimensionalized dynamics in Eq. (3) into a form more amenable to stability analysis. Then the equilibrium point of the transformed dynamics is computed and a coordinate shift is applied to move this equilibrium point to the origin. Finally global asymptotic stability of the origin is proven, which implies stability of the non-dimensionalized dynamics in Equation (3).

A. Transformed Leaderless Aggregate Dynamics
In this section, two assumptions on the model parameters are introduced.
Assumption 1: The network under consideration is leaderless, i.e., Note that this assumption is the same used in defining homogeneous consumer networks in [5]. Below, the networklevel dynamics will be derived by considering the new state variables z = log x and u = n i=1 y i .
In doing so the following assumption, which bounds the maximum possible value of ρ i for each agent, will be enforced.
Assumption 2: For all i ∈ {1, . . . , n}, ρ i ∈ (0, 2). Because ρ i is the normalized value of R i , Assumption 2 implies that R i ∈ (0, 2R max ). This is therefore a rather weak assumption as few agents are expected to have R i > R max because this implies that agent i's scarcity threshold is larger than the resource carrying capacity R max .

B. Leaderless Networks
Before deriving the modified network level dynamics of the system, this section considers Assumption 1 in more detail. First, we consider the existence of a leaderless dynamic.
Lemma 1: For any set of network weights ω ij , there exists a set of social orientations that renders the network leaderless.
Proof: Consider the matrix of edge weights, The leaderless condition is equivalent to W having a nontrivial null space. Notice that the matrix W T has rows that sum to 0, which implies that the vector 1 n is an eigenvector with eigenvalue 0. As W and W T have the same eigenvalues [22], W also has an eigenvalue at 0 and therefore a non-trivial null space. Then there must be a vector of normalized social orientation bv ∈ null(W ) and such a vector renders the network leaderless. Figure 1 shows two examples of a leaderless network for a set of uniform weights on a line graph and a cycle graph. Lemma 1 shows that any graph, including those commonly found in complex networks such as scale free [23] and small world [24] networks, can be rendered leaderless by the appropriate social orientation. As such, Assumption 1 is widely applicable. The behavior of the natural resource dynamic over a leaderless network will be further studied in Section IV, after the stability of the system has been established.  Fig. 1: 2 Leaderless Networks: a line graph (1a) and a cycle graph (1b). Each edge is labeled with its edge weight ω ij and each node is labeled with its social attribution b i v i .

C. Dynamics
With these assumptions in place, the transformed network level dynamics will be derived. Computing the time derivative of z giveṡ Differentiating u with respect to time and expanding giveṡ where the sum containing y i has vanished due to Assumption 1. Continuing, where From these definitions, K 1 is manifestly positive because it is a sum of positive terms. Under Assumption 2, it also follows that where the last inequality follows from Assumption 2.
The (z, u) dynamics thus take the forṁ Next, the equilibrium of the (z, u) system is computed in order to translate this system into one whose equilibrium is at the origin.

D. Equilibrium
The following lemma provides the uniqueness and value of the (z, u) system's equilibrium point.
where setting z = z 0 results iṅ Solving for u 0 then provides By Lemma 2, the equilibrium value of the resource, R 0 , (in the coordinates of Eq. (3)) is If K 2 > 0, which corresponds to at least one agent having R i > R max , then R 0 is larger than R max . This occurs as the agents with R i > R max will work to increase R beyond R max . Alternatively, if K 2 is negative then R 0 is smaller than R max , though R 0 is always positive because |K 2 | < K 1 and thus corresponding to a net effort to increase the available quantity of resource, while K 2 < 0 causes u 0 < 0, which corresponds to active resource consumption at steady state.
Having computed the equilibrium point of the system, we define a coordinate shift by where we have used e z0 = K 2 /K 1 + 1.
For w, the dynamics are governed bẏ

The final system dynamics to be analyzed arė
whose unique equilibrium point is the origin.

E. Global Stability
The following theorem demonstrates asymptotic stability of the system in Equation (5) to the origin.
Theorem 1: Under Assumptions 1 and 2 the origin is globally asymptotically stable in Equation 5.
Proof: Consider the Lyapunov function which is positive definite, satisfies V (0, 0) = 0, and is radially unbounded. Differentiating V with respect to time, Here, LaSalle's invariance principle can be used to prove global asymptotic stability of (0, 0) by showing that the set contains only the trivial trajectory v(t), w(t) ≡ (0, 0) [25].
To do so, observe thatV (v, w) = 0 for all trajectories of the form (0, w). Plugging this into the system dynamics in Equation (5) Then the only invariant point in V 0 has w = 0 becausev = 0 must hold to ensure that the system remains in V 0 .

IV. SIMULATIONS
This section considers the behavior of leaderless network topologies in simulation, focusing specifically on the case of the star graph. The star graph, also known as a hub, is of central importance to the study of complex networks [26]. The star graph also has a node, the center of the star, that might be expected to be the leader of a social network. Despite this, there are many leaderless social networks that can evolve over the star graph. Three leaderless networks on the same star topology are shown in Figure 2.
The resource was assumed to have a carrying capacity R max = 1, a growth rate r = 1, and a random initial condition that was fixed across simulations. The network was run with an ecological attribution a and a set of thresholds R where The time history of the resource level was identical for all 3 systems and is shown in Figure 3. The individual usages for each of the 3 systems are shown in Figure 4.

V. DISCUSSION
For each leaderless network considered here the aggregate resource consumption is identical, however the individual usage changes dramatically for the various weighting schemes. Further, given that the form of the individual consumption effort given in Eq. (2) is similar to the consensus dynamic [13], [14], it is reasonable to expect that individual consumption converges to a single uniform steady-state usage as happens under consensus on a connected graph.  this model addresses a need for social models that do not reach consensus [27].
To see why this behavior occurs, first note that the model allows negative resource usage and that stability of the equilibrium point requires that an agent (here agent 4 as shown in Figure 4) contributes resource to ensure balance with the usage of the other agents. As the network is leaderless, the equilibrium behavior of the system depends on the ecological component. Agent 4 has a threshold, R 4 = 1.17, which is significantly higher than the thresholds of its neighbors. This higher threshold drives the agent to contribute resource to balance out the usage of the agents that have lower thresholds and which therefore consume the resource. While this system is stable, as shown by Theorem 1 and displayed in Figure 3, this system level behavior would be worrying as the progress of a natural resource. Imagine, for example, the panic of a populace if the level of the local water reservoir were to change as indicated in Figure  3: The reservoir shifts quickly from being almost empty to overflowing and then starts heading back down towards empty before reaching equilibrium.
The issue raised in the preceding paragraph points to the fact that stability, while vital for understanding the behavior of a system, is not the only property of a natural resource system which must be understood. There are other questions, those related to sustainability, which must be addressed about these models before they are used to inform decision making in resource governance problems. For example, can humans use this resource in the short term without risking the depletion of the resource in the long term? Future work is required to bridge this gap between stability tools and the characterization of an ecological system as sustainable.

VI. CONCLUSION
In this paper, a model of natural resource consumption was considered. Stability was shown under the assumption that the network is leaderless and that the individual thresholds are in (0, 2R max ). The stability of the system was verified in simulation and it was shown that while the system is stable it is not necessarily sustainable.