WHY THE HERDER PROBLEM IS NOT A PRISONER'S DILEMMA ...

Daniel H. Cole and Peter Z. Grossman

INSTITUTIONS MATTER! WHY THE HERDER PROBLEM IS NOT A PRISONER’S DILEMMA

Abstract In the game theory literature, Garrett Hardin’s famous allegory of the “tragedy of the commons” has been modeled as a variant of the Prisoner’s Dilemma, labeled the Herder Problem (or, sometimes, the Commons Dilemma). This brief paper argues that important differences in the institutional structures of the standard Prisoner’s Dilemma and Herder Problem render the two games different in kind. Specifically, institutional impediments to communication and cooperation that ensure a dominant strategy of defection in the classic Prisoner’s Dilemma are absent in the Herder Problem. Their absence does not ensure that players will achieve a welfareenhancing, cooperative solution to the Herders Problem, but does create far more opportunity for players to alter the expected payoffs through cooperative arrangements. In a properly modeled Herder Problem – along the lines of an assurance game – defection would not always be the dominant strategy. Consequently, the Herder Problem is not in the nature of a Prisoner’s Dilemma.

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Electronic copy available at: http://ssrn.com/abstract=1114541

1. Introduction In the game theory literature, the Herder Problem (HP)1 is treated as a variant of the standard Prisoner’s Dilemma (PD) (see, e.g., Alcock and Mansell 1977, p. 444; Richards 2001, p. 621). There is nothing unusual in this; all manner of collective-action problems are brought within the rubric of the PD. This paper argues, however, in the context of the HP, that the broad application of the label “PD” is misleading. As Axelrod (1984, p. 11) notes, “[a] variety of ways to resolve the Prisoner’s Dilemma have been developed. Each involves allowing some additional activity that alters the strategic interaction in such a way as to fundamentally change the nature of the problem.” 2 In effect, a PD with an altered institutional structure, such that cooperative solutions are possible, is no longer a PD. If we reserved the label “Prisoner’s Dilemma” for games in which the payoffs and interactions of players naturally, or are institutionally biased to, favor a consistent dominant strategy of confession/defection, then the HP is not a PD. The HP and PD are different in kind because of a crucial difference in institutional structure: in the HP communication between players is not institutionally obstructed, as it is in the PD. Herders may or may not communicate, and communication may or may not result in a cooperative, social welfare-enhancing solution to the collective-action problem. But the mere possibility of communication creates the potential for cooperation, which differentiates the HP, in theory as well as in practice, from the PD. After explicating the crucial differences between true PDs and the HP, this paper discusses important implications of those differences and offers some advice to model builders for constructing a more realistic version of the HP, based on “assurance games,” that can be tested in experiments and against empirical situations.

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The Herder Problem is sometimes referred to as a Commons Dilemma (see Goetze 1994) or Commons Game

(Hope and Stover, 1982). 2

Emphasis added.

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Electronic copy available at: http://ssrn.com/abstract=1114541

2. The Conventional Treatment of the PD and HP in the Game Theory Literature a. The PD in Game Theory The PD is fundamental in game theory. Tom Schelling (1960, 214) defines it as “a configuration of payoffs that gives both players dominant incentives – in the absence of an enforceable agreement to the contrary – to choose strategies that together yield both players a less desirable outcome than if both had made opposite choices.” The classic example, from which the PD derives its name, concerns the strategic decision-making of two prisoners suspected by the police of some crime. The police have enough evidence to convict both prisoners of a minor offence,3 but confession by one or both of the prisoners would allow conviction for a more serious offense, with a longer prison sentence. To improve the chances of obtaining a confession from one or both of the prisoners, the judicial system structures the incentives of the prisoners by deliberately adjusting the penalties as follows: If neither prisoner confesses (both remain silent), each will be imprisoned for 3 years; if either one of the prisoners confesses, while the other remains silent, the confessing prisoner will go free, and the non-confessing prisoner will be sentenced to 10 years in prison; finally, if both prisoners confess, each will be sentenced to 6 years in prison. Thus, the familiar payoff matrix of the PD: Prisoner 2 Silent

Confess

Silent

-3,-3

-10,0

Confess

0,-10

-6,-6

Prisoner 1

3

This must be the case because if the police did not have enough evidence to convict the prisoners of any offense,

absent a confession, the payoff if both parties remained silent would be 0,0, significantly reducing incentives to confess.

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Crucially, the prisoners are separated and prevented from communicating with one another (see, e.g., Rapoport and Chammah, 1965, p. 228-229), so that they cannot agree to a cooperative arrangement in which neither confesses. This institutional structure ensures that each prisoner’s dominant strategy remains confession, though the collectively optimal strategy – the strategy that minimizes the penalty for both – is for neither to do so. The dominant strategy is a stable Nash equilibrium.4 It has been argued that the prevention of communication is not strictly necessary to the PD because any agreement between the prisoners would not be enforceable. This is the so-called problem of “cheap talk” (see, e.g., Farrell and Rabin, 1996): even if the players agreed to remain silent, the structure of payoffs would induce each of them to breach the agreement and confess. Were that actually the case, we might reasonably wonder why game theory models of the PD always call for the prisoners to be prevented from interacting, and why, as a matter of policy, police separate prisoners and prevent them from communicating with each other.5 Perhaps the police understand better than some game theorists that prisoners do not require enforceable contracts for cooperation to succeed; in fact, they do not need to talk at all. If, for example, prisoners were interrogated together, rather than separately, so that they could observe one another’s behavior, they might each engage, without any explicit agreement, in a tit-for-tat strategy, remaining silent so long as the other remained silent (see Axelrod 1985). Likewise, if communication between the two prisoners were not institutionally prevented, each might articulate a credible threat that confession by the other would eventually be punished. Indeed, an explicit threat might not even be necessary to engender in each prisoner a belief about retribution. Unilateral threats do not, of course, constitute enforceable contracts, i.e., they are in the nature of “cheap talk.” Yet, they may yield a “cooperative” solution, for “fear of reprisal is a

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For introductions to the basic PD game, see, e.g., Dixit and Nalebuff (1991, 12-14); Baird, Gertner, and Picker

(1994, 33); Poundstone (1992); Rapoport and Chammah (1965). 5

See, e.g., Laming (2003, p. 188) (“when police have two or more suspects arrested under suspicion of involvement

in the same crime, they interrogate them separately, keeping them always apart”); Inbau and Reid’s (1967, p. 85) classic manual on obtaining confessions through interrogations, specifies that the first rule in obtaining confessions from co-offenders is to “keep the subjects separated from sight and sound of each other….”

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very powerful motive…” (Staff of the Law-Medicine Center, 1962, p. 254). Thus, the institutionalized separation and prevention of communication between prisoners retains great practical importance both for models of the PD and in police interrogation policy.6 b. The HP in Game Theory As in the PD, the conventional HP involves two players making strategic decisions to maximize individual welfare in circumstances where the dominant strategy appears to be the opposite of the collectively rational strategy. In this context, the players are not prisoners with a binary choice of confessing or remaining silent; they are cattle ranchers with a binary choice of increasing or not increasing the size of their cattle herds on an open-access pasture. 7 The HP is derived from Garrett Hardin’s (1968) famous allegory of “The Tragedy of the Commons” (Pearce and Warford 1993, p. 247). Hardin posits an open-access pasture that inevitably will be over-exploited unless access and use of the pasture are restricted by the imposition of property rights or some form of government regulation. The “tragedy” ensues because each self-interested herder gains more from adding cattle to her herd, than she loses from the decreased marginal weight and market value of each head of cattle. She realizes virtually all the gains from her decision to add cattle to the pasture, but bears only a fraction of the losses in common with all the other herders. So long as access to and use of the pasture remain unlimited, and the expected net value of adding another head of cattle remains positive, each rational rancher will continue adding cattle, even if they recognize that the result is the unsustainable, over-exploitation of the pasture.8

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For further empirical and experimental evidence that “cheap talk” is not, in fact, cheap when it comes to resolving

HPs, see infra. 7

An open-access resource is one in which no individual has the right to exclude any other individual or group. On

the nature of open-access resources, and an exploration of Hardin’s theory of the “tragedy of the commons,” see Cole (2002, 5-16). 8

As Cole (2002, 6) explains, even a committed conservationist would likely continue adding cattle to the herd under

conditions of open-access because she could not enforce her conservation decision against any other herder. Others could, and presumably would, take up opportunities for additional profits that the conservationist so nobly left on the

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In its traditional game-theoretic variant, as described by Ostrom (1990, 3-4),9 the HP involves two herders, each attempting to maximize private revenues from grazing cattle on the openaccess pasture. Each herder decides to add or not add another head of cattle to her existing herd based on expected net revenues. Because the open-access pasture is finite in size and fecundity, the addition of each additional unit (head) of cattle reduces the grass available for all other cattle, resulting in smaller, marginally less valuable cattle. As in the traditional PD, each herder can choose one of two strategies, which in this case are labeled “cooperate” and “defect.” If both herders cooperate, they each earn 10 units of profit; if one cooperates while the other defects, the defector earns 11 units of profit, while the cooperator (the “sucker”) suffers a net loss of 1 unit of profit. Finally, if both herders defect, each realizes zero profit. The presumed payoff matrix is as follows: Herder 2 Cooperate

Defect

Cooperate

10,10

-1,11

Defect

11,-1

0,0

Herder 1

With these payoffs, the HP looks like a simple variation on the traditional PD. In both cases, the collectively optimal strategy is cooperation, which in this case would yield a joint profit of 20;

table. The conservation decision would turn out to be futile. However, as I explain in the next section, there is no institutional mechanism preventing the herders from communicating with one another and choosing, as a group, to alter the existing open-access regime to one of limited access and use. That possibility is what makes the HP fundamentally different from the PD. 9

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Dawes (1973; 1975) first characterized the HP as a form of PD.

but the individually dominant strategy is defection (see Goetze 1994, p. 7910). The mathematics is unassailable, the incentives insuperable. 3. Why the HP Is Not a PD But the PD-based payoff matrix is not a fair representation of the HP, even allowing for the necessity of simplification and stylization. In the PD, and the PD-version of the HP, the dominant strategy must always be defection, but even Hardin (1968, p. 1247) expressly noted that the “tragedy of the commons” could be successfully resolved by “mutual coercion, mutually agreed upon.11 Given that, defection cannot always be the dominant strategy in an HP. Thus, the very foundation upon which the conventional HP game supposedly rests (Hardin 1968) does not support the HP as PD. Moreover, unlike the standard PD, HPs are always iterative or repeat-play games in which communication, learning, and cooperation are not institutionally obstructed. Indeed, in real-world HPs, communication and learning are virtually certain to take place. Because HP games tend to be iterative, any simple 2-by-2 matrix is unlikely to capture the true structure of payoffs over time, as communication and learning ensue, creating opportunities for cooperation. And because cooperative solutions to HP games sometimes succeed and sometimes fail (see Ostrom 1990), the presumption of a constant or regular payoff structure creating a consistent dominant strategy is unwarranted. As games, HPs are far more complex than the game-theory literature has recognized. They are not simple variants of the standard PD. In the PD, cooperation between the two prisoners is rendered impossible or ineffective by two factors: (1) the payoff structure (i.e., incentives) favoring non-cooperation; and (2) the virtual impossibility of communication between the prisoners. Importantly, in the traditional PD, each of these factors is institutionalized. The police physically separate co-suspects to prevent them

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While Goetze (1994) recognizes that defection is the dominant strategy for the HP, he also points out that the

incentive structure of the HP game “has a feature qualitatively distinct from … a PD game” (p. 79), which is the subtractibility of the pasture. 11

Unfortunately, Hardin limited cooperative solutions to privatization or government regulation of access and use,

neglecting the possibility of local self-government, i.e., self-regulation by the resource users themselves (see, e.g., Ostrom 1990).

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from communicating with one another; and the payoffs (denominated in prison terms) are institutionally structured to create positive incentives for confession (“If you confess and your friend doesn’t, you’ll get a lighter sentence or even go free.”). In the HP, by contrast, there are no police officers or other organizations deliberately preventing the herders from meeting and talking.12 Even if the incentives created by the perceived payoffs initially favor defection, those payoffs are not deliberately established and structured to prevent cooperation. Rather, they reflect market forces under circumstances of open access. Over time, mutual observation and communication among neighboring herders is not just possible but entirely likely and could well alter the expected payoffs. Herders who would not voluntarily sacrifice any units of profit in the absence of communication and cooperation, might be willing to trade off one or more units of profit to secure the long-run conservation of the pasture pursuant to universal (or nearly universal) agreement to limit access and use. A self-imposed property/regulatory system could well alter the payoff structure, especially in circumstances where the behavior of other herders is easily monitored and effective sanctions are available to impose on defectors. In addition, because the HP is a repeat-play game and because social norms matter, the herders might positively value cooperation independently of the payoffs from grazing. Ostrom (1990, p. 15-17) observes that herders “can make a binding contract to commit themselves to a cooperative strategy that they themselves work out.” In fact, a cooperative strategy becomes increasingly likely among herders “who use the same meadow year after year, [and] have detailed and relatively accurate information about carrying capacity. They observe the behavior of other herders and have an incentive to report contractual infractions…. The selfinterest of those who negotiated the contract will lead them to monitor each other and to report observed infractions so that the contract is enforced.” This is precisely how many common-pool

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In this respect, PDs might be more realistically modeled as 3-person games, with the two prisoners and the police

as strategic players. The police, pursuant to their own dominant strategy to maximize convictions of arrestees, structure the interactions between the two other players by institutionalized limitations. The HP is, of course, different. There is no third party in the role of the police interposing institutional limitations on the interactions of the two (or more) herders.

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resource issues have been sustainably resolved around the world for centuries – a result that defies the unique dominant strategy of the standard PD. In Governing the Commons (1990), Ostrom’s primary concern was not to articulate the proper relation between the HP and the PD as games, but to (1) argue that common-property regimes are sometimes (more often than we might suppose) viable alternatives to either individual, private-property regimes or state regulation, and (2) explore the factors that seem to explain the success or failure of common-property regimes. Nevertheless, her analysis of local commonproperty regimes – regulation of access and use by the local users themselves pursuant to voluntary agreements – logically requires that communication and cooperation are both possible. As noted above, they are possible for an HP but not for a one-shot PD. Were herders subject to formal institutional arrangements that separated them and obstructed communications between them, like the prisoners in the standard PD, Ostrom’s argument about the viability of commonproperty regimes as solutions to real-world HPs would be a non-starter. Real-existing commonproperty regimes, of the kind Ostrom (1990) describes, would remain both unexplained and inexplicable. 4. Accounting for Institutions in Game Theory Models If the HP were a true variant of the PD, we would expect virtually all efforts to avert the “tragedy of the commons” by self-regulation to fail for lack of communication and cooperation because defection would always remain the dominant strategy (based on the payoffs). That is not, however, what we find empirically. While it is true that many efforts to manage common-pool resources fail for reasons of noncooperation, other efforts succeed (Ostrom, 1990, describes both successes and failures). Successful efforts by local user groups to conserve common-pool resources over long periods of time constitute solutions of the HP, and suggest that defection may not always be the dominant strategy. Thus, the conventional portrayal of the HP in the game theory literature is over-simplified.

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Defection as a dominant strategy in HP games is difficult to square, for example, with successful fisheries management regimes in places as diverse as Turkey and Brazil. An open-access fishery is a standard example of the HP; it differs from Hardin’s original only superficially. The fishers deplete the fishery by extracting too many fish, while the herders deplete the pasture by introducing too many cattle. Both cases involve scarce resources: pasturage and fish. In both cases, the initial starting point is open-access; any herder can graze as many head of cattle as she chooses, and any fisher can take as many fish as he chooses. The incentives in both cases are similar in that they are not deliberately constructed to ensure a certain outcome but market determined. Like the herders, but unlike the prisoners in the PD, fishers can communicate with one another and choose whether or not to cooperate. And the result for the open-access fishery is the same as the result for the open-access pasture in Hardin’s allegory: unsustainable overexploitation unless the users or governors introduce a property rights/regulatory regime to limit access and use. On the simple HP model, with a payoff matrix as above, the result surely would be a tragedy of the open-access fishery. But contrary to the simple HP model, the result for at least some open-access fisheries has not been tragic. In some fisheries, cooperation is the norm and defection a rare exception, defying the presumed payoff matrix of the simple (or simplistic) HP game. For instance, at the Alanya and Çamlik Lagoon fisheries in Turkey, fishers have cooperated to change the institutional structure in a way permitted in HP games, but not in PD games. They have replaced the initial open-access regime – characterized by no formal institutional structure – with a regulated-access regime, which has successfully conserved fishery resources over time. The fisheries at Alanya and Çamlik Lagoon have experienced “no decrease in overall catches over the years, no sharp drops in the catch per unit of effort, no obvious overcrowding of the fishery area, and no indication of vessels and fishermen dropping out of the fishery” (Berkes, 1992, p. 167). Those Turkish fisheries, and numerous other stories of successful resolutions of real-world HPs,13 illustrate that the HP cannot

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See, e.g., Bromley ed. ( 1992), Ostrom (1990), Ostrom and Gardner (1993), MaCay and Acheson eds. (1987);

Dahlman (1980).

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simply be a variant of the standard PD, where communication and cooperation are deliberately prevented. What, then, explains the significant difference between them? As Douglass C. North (1990) observes, institutions shape the payoffs, incentives, and dominant strategies of players in all games, not least in PDs and HPs. As we have seen, by changing the institutions, we change the payoffs, incentives, and dominant strategies. If institutional devices did not (a) prevent prisoners from communicating and cooperating, while (b) deliberately creating incentives for confession, there might well be no prisoner’s dilemma. The dominant strategy of confession only remains a dominant strategy because of institutions deliberately deployed by the criminal justice system to prevent prisoners from cooperating. In the case of HPs, no deliberately designed institutional structure prevents communication and cooperation; to the contrary, “open access” describes the very antithesis of a formal institutional structure.14 Communication and cooperation are neither promoted nor prevented (though informal institutions might create generate either positive or negative incentives). That is what makes the HP different in kind from PD. Because the players in an HP are not institutionally prevented from communicating and cooperating, they may (or may not) do so. Presumably, the lower the transaction costs, and the higher the gains from trade, the more likely cooperation will be (see Coase 1960). As a consequence, we cannot really know the dominant strategy for any particular HP in the absence of information that cannot be provided in a simple, 2 x 2 payoff matrix.

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This is not to say that players are not affected by any institutions; certainly, they are affected by informal

institutions, such as local customs. There are, however, no formally instituted impediments to communication and cooperation.

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5. A Better Model: The HP as an “Assurance” Game This section offers some advice to model builders on how they might construct an improved alternative to the simple-form HP model described by Ostrom (1990, pp. 3-4). Modelers do not need to start entirely from scratch. What Amartya Sen (1967) has labeled the “assurance problem” (a.k.a., “assurance game”) already accounts for some, but not all, of the variables relevant to the HP. What distinguishes assurance games, such as the “Stag Hunt” (see, e.g., Skryms 2003), from PDs is the existence of two equilibria, one of which represents “payoff domination” (the upper left-hand quadrant) and the other “risk domination” (the bottom righthand quadrant). Where assurance is insufficient to create confidence that others are doing “the ‘right’ thing,” cooperative solutions will fail, as in the PD, and players will seek to minimize their risk of loss. But, unlike the PD, the assurance game creates at least the possibility that the players can successfully assure each other than they “are doing the ‘right’ thing.” If such assurances prove credible, “then it is in one’s own interest also to do the ‘right’ thing” (Sen 1967, p. 122). In the context of the HP, the “right” thing can be taken to mean restricting herd size to conserve the pasture. An improved HP model should have the following elements: 1. The game can be with any number of players, N = 2 ….i, all making decisions about adding cattle to a congestible pasture of fixed size and fecundity, which at the start must be open access (not common property15). 2. The game is iterative. At each stage, each herder makes a decision to add or not add one more head of cattle to the herd. Because the pasture is congestible, each herder experiences costs whenever another head of cattle is introduced to the pasture, beyond the congestion point. Those costs, which are distributed equally between the players, are rising with the rate of congestion, so that at some point – presumably the point at which Hardin’s (1968) “tragedy” would occur – the

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On the critical distinction between open-access and common-property regimes, see, e.g., Cole (2002, p. 11).

private costs of adding an additional head of cattle to the herd would exceed the benefits for each herder. At that point, of course, the dominant strategy for all players would be to add no more cattle to the herd. 3. At each decision node players face a new set of payoffs depending on the choices made at each previous node. Decisions will depend on whether players know the strategy set for all other players, on whether they know the utility functions of the other players, on the completeness of knowledge about the consequences of adding, on the degree of risk aversion of the other players, and so on. In any case, choices at each node will affect incentives for reaching a cooperative solution to the HP. 4. All players are assumed able to communicate with all other players in the game. Communication can only be initiated, and agreements enforced, only by players in the game. That is, there is no outside institution or organization that brokers, enforces, prevents, or obstructs an agreement between the players. 5. Depending on assumptions about what the players know at the outset, communication may increase knowledge of other players. That is, probabilities of cooperation or defection are known with increasing certainty as the iterative game proceeds. This kind of Bayesian learning process suggests that a full model of the HP would provide an opportunity for players to predict future payoffs and thus alter informal institutional arrangements in ways that might guarantee long-run maxima. 6. Because the players are in close proximity to one another, can observe each other’s behavior at low cost, and interact over relatively long periods of time, reputational values might be incorporated into the model.16 The model might even include in players’ utility functions a value on cooperation for its own sake.

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On the potential importance of reputational effects in repeat-play games, see, e.g., Mailath and Samuelson

(2006).

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7. In a one-shot HP game, where N=2, the payoff structure would be assumed to possess the general form of an “assurance game,” where a > c ≥ d > b, and e > f ≥ h > g, as follows: Player 2 Left

Right

Up

a,e

b,f

Down

c,g

d,h

Player 1

In the specific context of the HP, the assurance game-based payoffs might be structured this way: Herder 2 Conserve

Add cattle

Conserve

p7,p7

-1,5

Add cattle

5,-1

5,5

Herder 1

In this form, there is uncertainty about the payoffs to conservation, represented by the probability p in the upper right-hand quadrant (0≤p≤1).17 The expected value of the payoff to cooperation for each party is affected by the perceived risk of defection by the other player. Thus, the expected value of conservation for both parties is a specified numeric payoff, 7, multiplied by the perceived probability that the other player also cooperates. If that probability is 1 or p = 1, the expected payoff equals 7. As the probability drops below 1, the expected value of cooperating to

17

Probabilities do not affect the payoffs in other quadrants because they are not subject to the uncertain variable of

assurance/trust.

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conserve the pasture falls. With payoffs as specified in the above matrix, so long as the probability of mutual cooperation remains above 0.715, conservation remains the dominant strategy for both parties. If the probability of mutual cooperation is exactly 0.7, the expected value from cooperation is only 4.9, which is lower than the payoff from defection (5). At that point (and at all probabilities lower than .7), adding another head of cattle to the herd would become the dominant strategy – sometimes referred to as the “risk dominant” strategy (Gardner 1995). As in Sen’s (1967) original model and in the conventional Stag Hunt game, mutual assurances in an HP game can increase the probability (p) of mutual cooperation, so that at high levels of p Conserve-Conserve is the “payoff-dominant” strategy. In the absence of such assurances, the probability of mutual cooperation might be reduced to such an extent that players choose the “risk-dominant” strategy of adding more cattle to their respective herds, preferring a smaller but certain gain over a possible loss. While the assurance game-based payoff matrix represents an HP more realistically than the PD versions so frequently found in the literature, the 2 x 2 form fails to account for the changing payoffs over time in iterative HP games, as communication and Bayesian learning ensue. In particular, the gains from adding cattle should decline over time as the pasture becomes increasingly congested. Meanwhile, the gains from conserving pasture should be rising as congestion increases. Nevertheless, the assurance game plainly provides a better starting point for modeling real-world HPs than the PD. The generalized assurance game provides a structure better suited to the HP than the standard PD because the assurance game allows but does not require trust relations, including assurances between players, to affect strategic interactions. Most importantly, the choice between payoffdominant and risk-dominant strategies will depend substantially on the credibility of assurances and the degree of certainty of the players. This is consistent both with Sen’s original statement of the “assurance problem,” and with the circumstances of actual common resource management decisions. If assurances of cooperation are believed, then the payoffs from cooperation to conserve the pasture dominate the payoffs from adding more cattle to the pasture. But if the

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assurances are insufficient or incredible and the long-run payoff structure is unclear, then the risk-minimizing strategy of adding more cattle dominates. 6.

Testing the Model

Once a better model incorporating the special variables of the HP is constructed, it can be tested in experiments and against real-world instantiations of HPs. Experiments might be structured to determine how HP games would play out in various circumstances (high vs. low transaction costs, high vs. low gains from trade, etc.). But those experiments should not be structured as ordinary PDs, in which the players are kept separate and incommunicado (as in Alcock and Mansell, 1977). To replicate a realistic HP scenario, the players must be allowed, but not required, to interact, communicate, and cooperate, (as in Hope and Stover, 1982, p. 388; and Edney, 1979). The importance of communication, even so-called “cheap talk,” to the resolution of HPs should not be underestimated. In a series of experiments based on variations on the HP, Ostrom, Gardner and Walker (1992; 1994) found that “subjects effectively used the opportunity for repeated cheap talk to increase joint returns from common-pool resources” (Ostrom and Nagendra, 2006, p. 19229). In one experiment, Ostrom, Gardner and Walker (1994) found that that changing just one variable – from no communication allowed to a single period of face-toface negotiations between the players – more than doubled joint returns from 21% of the maximum under no communication to 55% of the maximum with just one period of communication. Allowing face-to-face communication throughout all rounds of strategic decision making about resource use increased joint returns to 73% of the maximum (see also Ostrom and Nagendra, 2006, p. 19229). At least in the context of the HP, “cheap talk” can yield large returns.

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7. Conclusion This paper has shown that, contrary to its treatment in much of the game theory literature, the HP is not a variant of the PD but a distinct, more complex kind of game, in the nature of a repeatplay assurance game. To understand why, it is necessary to appreciate the crucial role that institutions play in structuring the payoffs that, in turn, create incentives for strategic choices. The standard PD arises in a highly structured institutional environment, in which potentially influential interactions among the players are strictly prevented by the game’s third player, the criminal justice system. In the HP, by contrast, formal institutions and organizations play little or no role in shaping the players’ behavior from the outset. Unlike prisoners, herders are free to communicate or not, and to cooperate or not (subject to informal institutions). The proper model of the HP must therefore be more complex and very different from the conventional PD. Author Contact Information Daniel H. Cole R. Bruce Townsend Professor of Law Indiana University School of Law – Indianapolis 530 W. New York St. Indianapolis, IN 46202-3225 [email protected]

Peter Z. Grossman Clarence Efroymson Chair and Professor of Economics Butler University College of Business Administration 4600 Sunset Ave. Indianapolis, IN 46208 [email protected]

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Acknowledgements The authors gratefully acknowledge the helpful comments and suggestions of William Bianco, Roy Gardner, Martin Holterman, Elinor Ostrom, Antony Page, James Walker, and R. George Wright. References Alcock, James E. and Diana Mansell. 1977. “Predisposition and Behavior in a Collective Dilemma.” Journal of Conflict Resolution 21:443-457. Axelrod, Robert. 1985. The Evolution of Cooperation. New York: Basic Books. Baird, Douglas G., Robert H. Gertner and Randal C. Picker. 1994. Game Theory and the Law. Cambridge, Mass.: Harvard University Press. Berkes, Fikret . 1992. “Success and Failure in Marine Coastal Fisheries of Turkey.” In Making the Commons Work, ed. D.W. Bromley, San Francisco: ICS, pp. 161-182. Bromley, Daniel W. ed. 1992. Making the Commons Work: Theory, Practice, and Policy. San Franciso, ICS Press. Coase, Ronald H. 1960. “The Problem of Social Cost.” Journal of Law and Economics 3:1-44. Cole, Daniel H. 2002. Pollution and Property: Comparing Ownership Institutions for Environmental Protection. Cambridge: Cambridge University Press. Dahlman, Carl. 1980. The Open-Field System and Beyond: Property Rights Analysis of an Economic Institution. Cambridge: Cambridge University Press. Dawes, R.M. 1973. “The Commons Dilemma Game: An N-Person Mixed-Motive Game with a Dominating Strategy for Defection.” ORI Research Bulletin 13:1-12. Dawes, R.M. 1975. “Formal Models of Dilemmas in Social Decision Making.” In Human Judgment and Decision Processes: Formal and Mathematical Approaches, ed. M.F. Kaplan and S. Schwartz, New York: Academic Press, pp. 87-108. Dixit, Avinash and Barry Nalebuff. 1991. Thinking Strategically: The Competitive Edge in Business, Politics, and Everyday Life. New York: Norton. Edney, Julian. 1979. “The Nuts Game: A Concise Commons Dilemma Analog.” Environmental Psychology and Nonverbal Behavior 3:252-254. 18

Farrell, Joseph and Matthew Rabin. 1996. “Cheap Talk.” Journal of Economic Perspectives 10:103-118. Feld, Barry C. 2006. “Police interrogation of juveniles: an empirical study of policy and practice,” Journal of Criminal Law and Criminology 97:219-316. Gardner, Roy. 1995. Games for Business and Economics. New York: John Wiley & Sons. Goetze, David. 1994. “Comparing Prisoner’s Dilemma, Commons Dilemma, and Public Goods Provision Designs in Laboratory Experiments,” Journal of Conflict Resolution 38:56-86. Hardin, Garrett. 1968. “The Tragedy of the Commons,” Science 162: 1243-8. Hope, Christine A. and Ronald G. Stover. 1982. Teaching Sociology, 9:383-399. Inbau, Fred E. and John E. Reid. 1967. Criminal interrogation and confessions. Baltimore: Williams & Wilkins Co. Laming, Donald. 2003. Understanding Human Motivation: What Makes People Tick? Boston: Wiley-Blackwell. Mailath, George J. and Larry Samuelson. 2006. Repeated Games and Reputations: Long-Run Relationships. Oxford: Oxford University Press. McCay, Bonnie J. and James M. Acheson (eds). 1987. The Question of the Commons: the Culture and Ecology of Communal Resources. Tucson: University of Arizona Press. North, Douglass C. 1990. Institutions, Institutional Change, and Economic Performance. Cambridge: Cambridge University Press. Ostrom, Elinor. 1990. Governing the Commons. Cambridge: Cambridge University Press. Ostrom, Elinor, James Walker and Roy Gardner. 1992. “Covenants With and Without a Sword: Self-Governance is Possible,” American Political Science Review 86:404-417. Ostrom, Elinor and Roy Gardner. 1993. “Coping with Asymmetries in the Commons: SelfGoverning Irrigation Systems Can Work,” Journal of Economic Perspectives, 7:93-112. Ostrom, Elinor, Roy Gardner, and James Walker. 1994. Rules, Games, and Common-Pool Resources. Ann Arbor: University of Michigan Press. Ostrom, Elinor and Harini Nagendra. 2006. “Insights on linking forests, trees, and people from the air, on the ground, and in the laboratory,” PNAS 103:19224-19231. Pearce, David W. and Jeremy J. Warford. 1993. World Without End: Economics, Environment, and Sustainable Development. New York: Oxford University Press. 19

Poundstone, W. 1992. Prisoner’s Dilemma. New York. Doubleday. Rapoport, Anatol and Albert M. Chammah. 1965. Prisoner’s Dilemma. Ann Arbor: University of Michigan Press. Richards, Diana. 2001. “Reciprocity and Shared Knowledge Structures in a Prisoner’s Dilemma Game.” Journal of Conflict Resolution 45:621-635. Sen, Amartya K. 1967. “Isolation, assurance, and the social rate of discount,” Quarterly Journal of Economics 81:112-124. Schelling, Thomas C. 1960. The Strategy of Conflict. Cambridge, Mass.: Harvard University Press. Skryms, Brian. 2003. The Stag Hunt and the Evolution of Social Structure. Cambridge: Cambridge University Press. The Staff of the Law-Medicine Center. 1962. “Psychology of Interrogation.” In Criminal Investigation and Interrogation, ed. S.R. Gerber and O. Schroder, Jr., Cincinnati: W.H. Anderson Co, pp. 247-285.

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