Abstract
Collaborative governance has become an essential strategy for addressing complex public challenges, yet its success often hinges on fostering cooperation among diverse stakeholders. This study applies the Stag Hunt framework from game theory to analyze the failure of Indiana's welfare modernization project, a high-profile example of contractual and governance breakdown. The case highlights critical lessons: the importance of trust, shared purpose, and well-structured contracts in sustaining cooperation; the risks posed by misaligned interests and rigid contractual mechanisms; and the challenges of managing multipartner collaborations. By bridging theoretical insights with practical applications, this research offers actionable strategies to design contracts that mitigate risks and enhance cooperation in collaborative governance arrangements.
Keywords
Introduction
Cross-sector collaboration is widely considered a necessary tool for tackling society's most complex public challenges. 1 Yet, for all its promise, collaborative governance is fraught with risk. Failure can lead to severe financial and social consequences, often borne by the most vulnerable citizens. 2 Empirical evidence confirms that many collaborative initiatives fail to achieve intended outcomes or incur costs exceeding those of alternative models. 3
Game theory effectively illustrates cooperation's fragile nature. The Prisoner's Dilemma (PD) models the temptation to cheat, showing defection to be the rational dominant strategy. 4 Heeding PD's lesson, practitioners often focus on deterring opportunism through contract penalties. However, the Stag Hunt game addresses a fundamentally different challenge: the uncertainty about others’ intentions. Here, defection is rational only if one doubts others’ commitment; then it becomes the safer choice. This shifts the central question from “How do we reduce the temptation to cheat?” to “How do we gain confidence that others will cooperate?” Consequently, the requisite contractual mechanisms (and strategies) shift from deterrence toward building trust and assuring partners of mutual commitment.
The distinction becomes even more critical, and dangerously overlooked, as networks expand through multi-tiered supply chains and subcontractor agreements. In the PD, adding players does not fundamentally change the incentive structure; each player retains a dominant incentive to defect. Yet, in the Stag Hunt, each additional partner multiplies uncertainty exponentially. The problem is compounded with the addition of more organizations to the governance network, where each link introduces its own doubts and risks.
The Stag Hunt demonstrates how each additional partner in a collaborative network exponentially increases uncertainty about others’ commitment, requiring a shift from deterrence-based contract design toward assurance mechanisms. We illustrate this dynamic with examples from a well-documented collaboration failure: the State of Indiana's welfare modernization project. This case makes the theoretical imperative concrete. By recognizing that commitment uncertainty requires different solutions, researchers, and practitioners can design governance mechanisms that prevent the type of breakdown that destroyed this billion-dollar partnership.
The analysis proceeds as follows: the next section reviews literature on collaborative governance and cooperation, followed by a narrative of the Indiana case. The Stag Hunt game is then outlined as a conceptual framework. The application section connects the case to the framework, and the article concludes with insights for refining contractual processes to foster the confidence needed for cooperative success.
Literature Review
While the terms “cooperation,” “coordination,” and “collaboration” are often used interchangeably in the literature on collaborative governance, their distinctions are critical. 5 Cooperation forms the essential foundation, referring to parties working together willingly in support of mutual, rather than purely self-interested, goals. 6 It is the “joint pursuit of agreed-on goal(s) in a manner corresponding to a shared understanding about contributions and payoffs.” 7 Coordination builds upon this, addressing the mechanics of how multiple parties align their activities to work together effectively. Collaboration represents the deepest level, where parties actively combine resources and expertise to create new solutions and jointly achieve shared goals. 8 This progression underscores that cooperation is a necessary, but not sufficient, condition for successful coordination or collaboration; it is both the starting point and a dynamic, ongoing element of any governance network.
The foundational work of Chester Barnard provides crucial insight into this dynamic. 9 Barnard maintained that cooperation enables organizations to achieve their aims, but contended that the structure and behavior of the whole emerge from the social traits of its subunits, specifically their culture, communication norms, and willingness to take risks (pp. 89–91). This principle is acutely relevant to collaborative governance, where a network's overall effectiveness depends on the capabilities and social dynamics of each organization. The challenge intensifies exponentially when primary contractors rely on subcontractors, as each new organizational link introduces its own unique properties and uncertainties. The resulting complexity is not merely additive; it is multiplicative, making it progressively more difficult to maintain the shared understanding and mutual confidence necessary for the entire network to function. This illustrates why adding organizations to a network is a fundamental reshaping of the collaborative endeavor, not just a matter of managing more relationships.
The high risk of collaboration failure has not gone unrecognized, with recent scholarly attention devoted to the propensity for conflict among diverse stakeholders. 10 In response, scholars have relied on several theoretical perspectives to manage these risks, though many implicitly address a bilateral, PD-like problem of deterring opportunism. Transaction-cost economics (TCE), for instance, focuses on designing contracts with safeguards, penalties, and flexibility to curb defection and adapt to unexpected changes. 11 Scholars have developed several theoretical perspectives to manage these risks, though many implicitly address a bilateral, PD-like problem of deterring opportunism. TCE, for instance, focuses on designing contracts with safeguards, penalties, and flexibility to curb defection and adapt to unexpected changes. 12 While TCE provides valuable insights for deterring opportunism, it is not as well-suited to address the cascading uncertainties of multi-tiered collaborations, where an equally important challenge is managing doubts about partners’ commitment and capability throughout the network or supply chain. Recognizing the limits of formal contracts, a robust strand of literature emphasizes that trust and relational norms are essential for filling contractual gaps and sustaining cooperation, 13 a concern closer to the assurance problem of the Stag Hunt.
Early work by Macaulay even argued that overly formal contract language can defeat the trust it seeks to enforce. 14 Likewise, behavioral research by Hart and his colleagues 15 shows how perceptions of unfairness lead to “shading,” conscious or unconscious actions that undermine collaboration. The consensus is that achieving collective benefits requires both selecting appropriate partners and actively building trust over time. 16 Networks are inherently unstable, prone to both reconfiguration and failure. 17
Yet, the literature offers fewer tools for how to build this trust systematically across a network or supply chain. For example, in public–private-partnerships (P3) primary contractors may hire subcontractors to deliver on some tasks, yet government, who is the buyer, may have no direct relationship with the subcontractors, despite their performance being critical to the overall effectiveness of the network.
Ultimately, while various governance mechanisms have been proposed, from contract flexibility 18 to management strategies such as negotiation and leadership, 19 cooperation remains the critical, fragile foundation for success. 20 Given that collaborative governance is defined by the interdependence of multiple organizations and the fundamental challenges of trust and reciprocity, game theoretic frameworks such as the Stag Hunt are uniquely capable of modeling the strategic dynamics that determine whether parties will choose cooperation or defection. To demonstrate this potential and illuminate the specific challenges of multi-actor uncertainty, we provide details of a complex public–private partnership in Indiana intended to modernize the state's welfare administration.
Case Study 21
Indiana's failed welfare modernization project illustrates how collaborative governance can collapse under cascading coordination failures rooted in Stag Hunt dynamics.
In 2005, Governor Mitch Daniels initiated an effort to centralize welfare claims processing through the Family and Social Services Administration (FSSA), a transformation no other state had successfully accomplished. In December 2006, Indiana awarded IBM a 10-year, $1.3 billion contract (Master Services Agreement, MSA) to lead a coalition of subcontractors known as the “Hoosier Coalition for Self-Sufficiency” to accomplish its goal. The MSA was negotiated by a team of attorneys; the final version is a complex document spanning more than 150 pages, with numerous exhibits and appendices. The project was to unfold in stages and region by region following a timeline, including transition-in phase before the project would reach a fully implemented “steady state.” 22 Affiliated Computer Services (ACS) held a critical role as the main subcontractor, overseeing 2,200 existing caseworkers. As many as eleven other subcontractor organizations were also part of the Coalition. The basic structure of the networked governance arrangement illustrated in Figure 1.

The network collaborative governance structure of the Hoosier coalition.
The potential payoff for key project participants was significant. The state expected over $340 million in savings. If all succeeded the Governor could showcase his modernization of the welfare system. IBM stood to gain over $1.3 billion in contract revenue; the company also invested considerably in dedicated hardware and software, approximately $12 million. Although the precise amount of the ACS contract is unknown, yearly reports from the Indiana Department of Administration reflect provide an estimate of over $300 million.
In clarifying roles and responsibilities, the MSA specified that the State would retain final authority in some areas, among them, policy-making and eligibility determinations. IBM bore “full responsibility and liability” for subcontractor performance (MSA sec. 3.7.2(7)(ii); sec. 14.1). Critically, the MSA also mandated that all communications flow through IBM (sec. 14.6.2). While this was ostensibly intended to maintain coordination, it did little to incentivize others in the coalition to stay committed. In fact, the subcontractors were not signatories to the MSA.
IBM's performance obligations were meticulously delineated in the MSA across four distinct categories, each tied to specific project phases: (1) Critical Transition Milestones, outlining objectives for staff transitions and software implementation; (2) Transition Key Performance Indicators (TKPIs), applied to select counties during the transition; (3) Steady State Key Performance Indicators (KPIs), effective after transition; and (4) Service Level Metrics (SLMs), governing operations during the Steady State phase (Dryer 2012, 30–31). The MSA permitted Indiana to terminate the contract for convenience without demonstrating fault. Yet, it also imposed substantial liquidated damages for performance failures: penalties ranged from $150,000 to $350,000 for Critical Transition Milestones, and from $500 to $5,000 for violations of KPIs, TKPIs, or SLMs. 23
Challenges emerged quickly. In 2008, rising demand for assistance from a recession, natural disasters, and a budget shortfall in Indiana, exposed uncertainties about each partner's capacity and commitment. During this period, ACS communicated regularly and directly with the state, bypassing IBM in violation of the MSA. ACS also lobbied the state to replace IBM. In one email, an ACS told Indiana FSSA Secretary Roob, “IBM really does not understand how to deliver social services.” 24 While this may have been an attempt by ACS to position itself favorably with the state, court transcripts reveal that its behavior eroded trust in the coalition. State witness Kelly Hanley testified that a key ACS employee was “uncommitted” and “had no idea of what was going on.” 25
Throughout the project's implementation, Indiana officials consistently assured the press that modernization was progressing successfully, despite mounting evidence of operational setbacks. This public optimism was juxtaposed with the evaluations of third-party monitor First Data Corporation, which issued “yellow ratings” in several performance categories requiring improvement. In 2008, Governor Daniels featured the project in his re-election campaign. By the end of 2008, the state expanded IBM's contract scope eleven times, augmenting its value by $178 million. These expansions functioned as tangible, yet contradictory, signals of the state's continued commitment to the coalition and its stability amid growing difficulties.
Such actions underscore the critical role of communication in sustaining complex organizational structures. 26 In this case, however, the signals coming from the state were mixed: public affirmations of success, monitor ratings indicating some deficiencies, and financial reinforcements of the contract. This inconsistent messaging likely added to uncertainty within the network regarding the actual state of the project and the commitment levels of its partners, ultimately undermining the very cooperation essential to the venture's survival.
In November 2008, IBM presented Indiana officials with a proposal for 17 reforms aimed at addressing mounting operational challenges within the project. 27 Coinciding with this effort, Governor Daniels appointed Anne Murray to replace Mitch Roob as director of the FSSA, a leadership transition that introduced significant uncertainty regarding the state's commitment to the existing partnership. As one key participant noted, “The beginning of the end was when the Governor named a new head of the FSSA.” Another observed that “the subcontractors were trying to figure out if the State was planning to end the contract early and whether they should pull out or stay.” The hedging behavior of some coalition members appears to be driven by both legitimate concerns over coordination and self-interested risk management. This dynamic illustrates a classic Stag Hunt scenario, in which the greatest risk lies in remaining committed while others defect. Without credible assurances of commitment, the coalition was destabilized. The uncertainty only grew in the remaining months of the project. In March 2009, Indiana sent the IBM Coalition a letter requiring a Corrective Action Plan (“CAP”) in order to address what it saw as the remaining problems in the project. 28 In September 2009, the state determined that the centralized system was not working and decided to adopt a new, hybrid approach to welfare modernization, Plan B (p. 63).
On October 15, 2009, less than 3 years into a 10-year contract, the coalition dissolved. FSSA Secretary Anne Murphy formally notified IBM of the state's decision to terminate the Master Services Agreement for cause, citing persistent failures in the “quality and timeliness” of service delivery (pp. 73–77). Paradoxically, on that same day, Governor Mitch Daniels publicly attributed systemic failures to the complexity of the modernization effort rather than to IBM. No doubt, the MSA's payoff structure failed to adequately reward cooperation or disincentivize defection. Financial and reputational consequences of failure were also asymmetrically distributed, with taxpayers shouldering the burden while employees and political actors remained insulated from accountability. As Judge Dryer proclaimed in the introduction of his Final order, “Both parties are to blame and Indiana's taxpayers are the losers.” 29
This termination and the ensuing litigation underscore how coordination failures in public–private partnerships can produce lose–lose outcomes, when the predominant or sole focus is on mitigating opportunism. The MSA was drafted according to a PD logic, relying on penalty clauses and performance metrics to deter opportunism. Yet, these conventional contractual mechanisms proved inadequate for mitigating the deeper coordination and assurance problems inherent in a multi-actor governance network. The structure itself engendered Stag Hunt conditions, wherein mutual success depended on each actor's confidence in the others’ commitment and competence. As Judge Bailey later noted, the state's relationship with subcontractor ACS constituted “an interdependent relationship that far exceed[ed] the more typical production scenario.” 30
While self-interested behavior may have played a role, the collapse also illuminates legitimate doubts among partners regarding each other's capabilities and willingness to fulfill complex, interdependent obligations. These doubts were compounded by inconsistent signals and information asymmetries throughout the network. Rather than receiving clear indications of mutual commitment, actors encountered contradictory messages that heightened uncertainty about both intent and capacity, thereby undermining the cooperation necessary for success.
The Basic Stag Hunt
Originally formulated by Jean-Jacques Rousseau, the basic version of the game presents a scenario where two hunters must decide whether to cooperate (hunt a stag) or pursue individual interests, the equivalent of noncooperation or defection (hunt rabbits). 31 In game theory, noncooperation is equivalent to defection. In the Stag Hunt, the hunters gain greater rewards from capturing the stag than from catching individual rabbits. Thus, the stag represents a high-reward but high-risk endeavor that requires cooperation, while rabbits represent a lower-reward but safer individual effort.
In the context of collaborative governance, organizations are the hunters and the stag represents a significant shared goal, such as upgrading and maintaining a toll road or implementing a work-release program to support the reintegration of formerly incarcerated individuals into society. These projects often require formal agreements between public and private sector organizations, where successful cooperation yields greater benefits for all parties compared to any organization pursuing individual objectives. 32 Rabbits symbolize the allure/temptation for organizations to prioritize less risky objectives by not cooperating. For private sector organizations, defection is tempting if more profitable opportunities become available. The public sector, on the other hand, might be inclined to defect if the political benefits diminish over time. The role of political support in government actions is crucial for successful collaborations. 33 The Stag Hunt can be illustrated in matrix form 1. 34
Referring to Table 1, each player must strategically decide whether to commit to the partnership (hunt the stag) or pursue individual objectives (hunt the rabbit), considering the potential risks and rewards. The risks and rewards are the potential payoff combinations in Table 1 relative to each hunter's decision (the gray areas of the table). Specifically, if both players (Hunters) opt for the stag (top left of the table) each receives a payoff of 5. If both give in to the temptation to catch a rabbit (bottom right of the table), the payoff for each is 2. However, if one player decides to go for a rabbit while the other decides to catch a stag (bottom left and/or top right of the table), then the first player receives a payoff of 4, and the second player gets no payoff at all (also called the sucker's payoff). The incentive structure can also be represented as follows:
The Basic Stag Hunt.
The Stag Hunt rewards mutual cooperation the most (R), followed by the equal outcomes of temptation and punishment (T = P), while the lowest payoff is given to the “sucker's payoff” (S), one player choosing to cooperate (hunt the stag) while the other choosing not to cooperate (hunt the stag).
In the game, there are two main winning strategies, known as pure Nash equilibria: the risk-dominant equilibrium and the payoff-dominant equilibrium. Playing it safe corresponds to the “Rabbit, Rabbit” strategy, which is risk-dominant, compared to the “Stag, Stag” strategy, which is payoff-dominant. Players must decide between these strategies by asking: Should I play it safe (the risk-dominant strategy) or aim for the highest reward (the payoff-dominant strategy)? This choice is driven by the certainty of a smaller reward from hunting the rabbit, as opposed to the risk of gaining nothing (sucker's payoff) while hunting the stag if the other player defects.
Comparing the different payoffs, it becomes clear that a player's decision on whether to cooperate or not depends on whether they have assurances with respect to the other player's intentions. The player is likely to choose to cooperate (hunt the stag) if certain the other player will also cooperate, which would result in a higher payoff for both. The player is more likely to choose noncooperation (hunt the rabbit) when uncertain about what the other will choose. To be sure, if one player knows or suspects the other player will defect, the rational choice is also to defect and hunt the rabbit; that is, to get something rather than nothing. Thus, the Stag Hunt game exemplifies the conflict between opting for a smaller but certain reward and the risk associated with pursuing a larger reward that requires mutual cooperation and a key to the game is to understand and know the other player's situation and intentions. In other words, when one player is assured that the other will proceed in good faith—that is, when commitments are perceived as credible—cooperation has a chance.
The basic game represented in Table 1 has a simplified payoff structure with values between 0 and 5, but it is not difficult to imagine how different payoffs can influence decisions. For example, the higher the value of joint cooperation (Stag, Stag) for both players compared to the payoff for any other outcome, the more likely they are to cooperate. However, if the payoff for joint cooperation is not much higher than the payoff for noncooperation, noncooperation becomes a more tempting option.
In summary, the structure of rewards and penalties in a collaborative governance arrangement heavily influences each party's decisions and, in turn, the project outcome. High rewards for cooperation encourage full commitment but require mutual trust. Moderate rewards for defection offer a safety net but reduce incentives for full collaboration. Severe penalties for mismatched efforts can deter risk-taking if trust is weak. Without strong trust and communication, parties may default to minimal effort, ensuring a guaranteed but lower benefit. This fallback option reduces risk but discourages full commitment and effort, limiting the project's potential success.
N-Party Stag Hunt: More Partners Increases the Risks of Cooperation
The basic game was presented to illustrate the basic lessons of the Stag Hunt. Ensuring cooperation in a multiparty Stag Hunt presents significant challenges due to the complexity of coordinating actions among all participants. In such scenarios, there is still no dominant strategy, but successful cooperation requires every participant to choose the Stag Hunt. The inclusion of even one defector disrupts the effort, resulting in a failed outcome for all. As the number of participants increases, so does the risk of failed coordination, as each additional player introduces more uncertainty. The payoff structure reflects this complexity: full cooperation yields the highest rewards (a stag share for all), but individual defection can lead to uneven outcomes where some hunt rabbits while others fail at stag. If all parties opt for rabbits, the rewards are lower than the Stag Hunt, but failure to achieve any cooperation leaves everyone with nothing. This delicate balance of trust and risk makes cooperation increasingly difficult to sustain in larger groups. The challenge is illustrated mathematically and in matrix form in Appendix 2.
While the three-player game shown in Appendix 2 highlights the challenges, imagine the difficulties and the changes in probable success if we added more players to the matrix. Indeed, most collaborative governance arrangements involve multiple partners and over time the membership organizations often change and reconfigure. 35 The matrix becomes exponentially more complex as we would have to account for every combination of players choosing to hunt the stag or rabbit, which can be quite extensive for larger groups. With just four players, the payoff for each player depends on the choices of all four players.
Application
The case evidence reveals the expected payoffs and the actual payoffs for the various parties involved in the project. Table 2 below summarizes the various elements of the payoff structure and the sources of selected evidence.
Indiana Welfare Modernization Project Main Parties’ Payoffs.
Applying the basic elements of the Stag Hunt to the Indiana case study, we can also summarize the parties’ strategy choices: to cooperate (payoff-dominant and hunt stag) or not cooperate/defect (risk-dominant and hunt rabbit) based on case evidence and the likely determinants of that choice (given the evidence of the possible intentions of other parties involved in the effort to modernize Indiana's welfare system). The summary appears in Table 3.
Indiana Welfare Modernization Project Main Parties’ Selected Strategies.
ACS: Affiliated Computer Services; FSSA: Family and Social Services Administration; MSA: Master Services Agreement.
The dates and occurrences outlined in Table 3 are all derived from court documents. As shown in Table 3 the State, including the Governor and FSSA Directors, were initially cooperative (Stag) but later shifted to self-serving behavior (Rabbit), evidenced by early satisfaction with the project and subsequent decisions to terminate the contract. Similarly, IBM shifted from cooperation (Stag) to defection (Rabbit), as seen in its initial investment and later demands for additional compensation for Plan B implementation. ACS engaged in self-serving behavior (Rabbit) from the start, as evidenced by direct communications with the state and knowledge of the Governor's declining commitment to the project. The summary demonstrates how changes in perceived intentions and strategic choices among parties contributed to a breakdown in cooperation, leading to the project's failure. It also emphasizes the role of signaling and misaligned incentives in fostering defection rather than collaboration.
Discussion and Conclusion
The Stag Hunt game theory framework significantly advances our understanding of collaborative governance failures by clarifying the core strategic dilemma at play. Unlike the PD, which centers on deterring opportunism, the Stag Hunt reframes failure as a problem of mutual assurance, where the primary risk is the fear of being the “sucker” who cooperates while others choose not to cooperate. Defection becomes rational only when actors doubt others’ commitment, shifting the central question from “How do we reduce the temptation to cheat?” to “How do we gain confidence that others will cooperate?” This framework's scalability to multi-actor settings directly addresses the complexity of modern collaborations, illustrating how each additional organization exponentially increases coordination risks. The Stag Hunt suggests that contracting must consider not only which organization should lead but how many are necessary, and how to maintain credible commitment across all partners to avoid cooperative breakdown.
Indiana's failed welfare modernization project serves as an ideal case for applying this model. Traditional transaction-based contracting, modeled on the PD, proved inadequate to address the assurance problems inherent in the Stag Hunt conditions of this network. Although the state may have been the first to defect (choose the Rabbit), ACS's attempts to replace IBM made the coalition more vulnerable. The fact that unequal power dynamics contributed to the collaboration failure is consistent with recent research. 36 Specifically, the evidence shows that these dynamics caused multiple organizations in the coalition to lose trust, a necessary condition for collaboration success. 37 The Master Services Agreement (MSA) prioritized compliance and penalties over shared purpose, failed to align incentives toward collective gains, and created asymmetrical accountability, where taxpayers bore costs while political and administrative actors remained insulated. Agreements for public–private partnerships are often overly rigid and faulty; many contain perverse incentives that undermine public interest. 38 This adds to the research on contract design for complex services 39 and research on structuring alliances. 40
Early violations, such as ACS bypassing IBM to communicate directly with the state, eroded trust and triggered a classic Stag Hunt dynamic: Each party, fearing defection by others, abandoned cooperation. The failure was not merely one of opportunism, but of a fundamental misalignment between contract design and the strategic requirements of multi-actor collaboration.
The Stag Hunt reveals that the central challenge in such collaborations is managing commitment uncertainty. In Indiana, confidence eroded through cascading doubts: subcontractors questioned the competence of the prime contractor, the state sent conflicting signals via simultaneous contract expansions and critical performance reports, and leadership changes introduced political uncertainty. The contract itself exacerbated these issues with its primary foci being compliance and penalty and little to no attention on the relational mechanisms necessary to sustain cooperation.
These insights carry clear implications for policy and practice. Contracts must be designed not only to penalize bad behavior but to foster good faith through structures that enable transparency, facilitate effective communication across the network, and supply credible signals of commitment. Joint governance committees and collective incentive structures can help sustain mutual assurance. Public managers must also recognize leadership continuity and consistent political messaging as critical governance mechanisms—not merely “soft” factors—that reduce strategic uncertainty.
Furthermore, governments must assess the vulnerability introduced by each subcontractor. Every entity in the supply network must reliably cooperate, yet the actions of the most obscure subcontractor can undermine the entire endeavor. Therefore, due diligence and assurance mechanisms—such as prime accountability for subs, joint monitoring, and subcontract transparency—must extend across all tiers. Incentive structures must be aligned network-wide, not only between government and prime contractor.
Future research should continue to integrate game theory and contract research, examining how different contractual levers, such as relational mechanisms and collective incentives, can reduce assurance problems in networks of varying size and complexity. The Stag Hunt provides a powerful lens for understanding why collaboration fails and how it might succeed. While the rewards of cooperation are great, they remain attainable only if we first build the confidence to hunt the stag together.
Footnotes
Funding
The authors received no financial support for the research, authorship, and/or publication of this article.
Declaration of conflicting interests
The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
Notes
Author Biographies
Appendix 1
Appendix 2
The table above is a simplified representation of a payoff matrix for a Stag Hunt with only 3 hunters/players to illustrate the various outcomes based on the decisions of each player. Each player can choose to hunt the stag (cooperate) or the rabbit (defect). The payoffs are assigned based on collective choices. Adding more players makes cooperation increasingly difficult. Referring to the matrix, “A” represents hunting the stag (cooperation). “B” represents hunting the rabbit (defection). The order of letters represents the choices of Player A, Player B, and Player C, respectively. This matrix shows the outcomes for each combination of choices. The highest collective payoff is achieved when all players cooperate (AAA). However, as with the two-player game, the risk of defection makes the highest collective outcome uncertain. The matrix illustrates the strategic considerations each player must make, balancing the potential for higher rewards against the risk of others’ defections. In this payoff structure, if all three players hunt the stag, each player gets three points. If two players hunt the stag and one hunts the rabbit: the stag hunters get 0, and the rabbit hunter gets 2. If one player hunts the stag and two hunt the rabbit: the stag hunter gets 0, and each rabbit hunter gets 1. If all three players hunt the rabbit: each player gets 1 point.
As with the two-player game, the payoff for successfully hunting the stag is significantly higher than pursuing the rabbit, but it requires all players to cooperate. If even one player defects, the cooperative effort fails, and those hunting the stag end up with nothing. This scenario introduces a greater risk of failure in cooperation, as the likelihood of at least one player defecting increases with more players. Specifically, as the number of players increases, the complexity of achieving unanimous cooperation also rises. This is primarily because each additional player introduces an additional risk of defection. In a scenario where all must cooperate to succeed (hunting the stag), the probability of at least one player choosing to defect (hunting the rabbit) generally increases with more players. In smaller groups, the impact of each partners’ choice is more pronounced, which can either hinder or help cooperation, depending on the players’ preferences and strategies.
However, there is more difficulty in coordinating and maintaining trust among a larger group. The three-player game highlights how individual incentives can undermine group cooperation, especially when the number of participants increases. This scenario is particularly relevant in collaborative governance arrangements, where multiple stakeholders must collaborate to achieve a common goal. The success of such ventures often hinges on the ability of the parties to trust each other and commit to the collective effort, despite the temptation of individual gains that might come from noncooperative actions.
The matrix for four players would be extremely large, as there are sixteen possible combinations of choices (Stag or Rabbit for each of the four players). In the Stag Hunt game with four players, several scenarios illustrate the dynamics of cooperation and defection. When all players cooperate by hunting the stag (Players A, B, C, and D choose Stag), each receives the highest payoff of 4, reflecting the benefits of full cooperation. However, if three players cooperate and one defects (Player D chooses Rabbit while the others choose Stag), the cooperating players end up with no payoff, and the defector gains a moderate payoff of 3. This scenario demonstrates the risk of cooperation when not all parties are aligned. In a situation where two players cooperate and two defect (Players A and B choose Stag, C and D choose Rabbit), all players receive a moderate payoff of 2, indicating a balance between cooperation and defection. When only one player cooperates and the other three defect (Player A chooses Stag, others choose Rabbit), the lone cooperator gets nothing, and the defectors each receive a payoff of 2, highlighting the vulnerability of unilateral cooperation. Finally, if all players defect by hunting the rabbit, they each receive a lower payoff of 1, showing the suboptimal outcome when no one opts for cooperation. These scenarios collectively underscore the complexities and strategic considerations involved in balancing individual and collective interests.
