Dark matters Exploitation as cooperation - Sustainable Consumption ...

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Dark matters: Exploitation as cooperation$ Partha Dasgupta a,b,n a b

Faculty of Economics, University of Cambridge, Cambridge, United Kingdom Sustainable Consumption Institute, University of Manchester, United Kingdom

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abstract

Keywords: Prisoners’ Dilemma Long-term relationships Nash equilibrium Min–max strategy Common property resources

The empirical literature on human cooperation contains studies of communitarian institutions that govern the provision of public goods and management of common property resources in poor countries. Scholars studying those institutions have frequently used the Prisoners’ Dilemma game as their theoretical tool-kit. But neither the provision of local public goods nor the management of local common property resources involves the Prisoners’ Dilemma. That has implications for our reading of communitarian institutions. By applying a fundamental result in the theory of repeated games to a model of local common property resources, it is shown that communitarian institutions can harbour exploitation of fellow members, something that would not be possible in societies where cooperation amounts to overcoming the Prisoners’ Dilemma. The conclusion we should draw is that exploitation can masquerade as cooperation. & 2011 Elsevier Ltd. All rights reserved.

1. Introduction The units that are subject to selection pressure in evolutionary biology are ‘‘strategies’’ (Maynard Smith, 1982; Nowak, 2006), which are conditional actions, such as, ‘‘Do w if P occurs, do x otherwise’’, or ‘‘Do y if the predator does Q, do z otherwise.’’ In contrast, the units studied in the social sciences select strategies from available menus so as to assist their projects and purposes. As agency assumes a central role in the social sciences, the units there are called ‘‘agents’’, or ‘‘parties’’. Sometimes we economists call them ‘‘people’’! Robinson Crusoe aside, people do not live in isolation. An agent’s best choice depends on other people’s choices. Moreover, as their projects and purposes involve not just the present but the future too, each agent can be assumed to reason about the likely present and future consequences of their respective choices, while recognizing that all others are engaged in similar reasoning. That is why beliefs about what others may do and what the consequences of those choices would be are at the basis of strategy selection. Social environments are inter-temporal games, in the sense of the theory of games.

cooperation. The first concerns the way the benefits and burdens of cooperation are to be shared. Traditionally, that problem has been studied under the name of ‘‘bargaining theory’’.1 Suppose, however, that the group has reached an agreement. Its members now face a second problem, which is to design a system of incentives, involving rewards and punishments, under which each person can trust everyone to do what is expected of him or her under the terms of the agreement. In recent years it is the latter problem that has been the focus of the many social scientists who have studied communitarian modes of governance in various parts of the world.2 The two problems are related. It would, for example, be foolish of a group of people to agree to a course of action if members are unable to institute a system of incentives under which the agreement would stick. But there are analytical advantages in keeping the two separate. So I follow the many scholars who have studied communitarian governance empirically (e.g., Ostrom, 1990; Baland and Platteau, 1996) and those who have studied it theoretically (e.g., Fudenberg and Maskin, 1986; Mailath and Samuelson, 2006), by taking agreements as given. What I explore are systems of governance under which members can trust one another to abide by the terms of their agreements.

2. Framing the problem of cooperation There are two inter-related problems besetting any group of people who have discovered that there are gains to be had from $ For their comments on an earlier version of the paper, I am most grateful to two anonymous referees. n Correspondence address: Faculty of Economics, University of Cambridge, Austin Robinson Building, Sidgwick Avenue, Cambridge, Cambs CB3 9DD, United Kingdom. Tel.: þ 44 1223 335227. E-mail address: [email protected]

1 Bargaining theory has a long history and has been developed along two alternative lines. Luce and Raiffa (1957) remains a remarkable book-length treatment of ‘‘axiomatic bargaining theory’’. For studies in ‘‘strategic bargaining theory’’, see Rubinstein (1982) and Ray (2008), among others. See also Binmore and Dasgupta (1987) for a discussion of the methodological differences between the two approaches. 2 The literature is gigantic. For book-length expositions of village level casestudies, most often in poor countries, see Wade (1988), Ostrom (1990), and Baland and Platteau (1996).

0022-5193/$ - see front matter & 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.jtbi.2011.04.020

Please cite this article as: Dasgupta, P., Dark matters: Exploitation as cooperation. J. Theor. Biol. (2011), doi:10.1016/j.jtbi.2011.04.020

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P. Dasgupta / Journal of Theoretical Biology ] (]]]]) ]]]–]]]

Imagine a group of people who have agreed to cooperate on a venture and share the resulting benefits and burdens in a specified manner. If the parties do not trust one another, what could have been mutually beneficial transactions will not take place. But what grounds could they have for trusting one another to do what they have undertaken to do? They would have grounds only if promises were credible; mere assurances would not be enough (witness that we tell others, and ourselves too, not to trust people ‘‘blindly’’). However, if the parties are to trust one another to keep their promise, matters must be so arranged that (i) at every stage of the agreed course of actions, it would be in the interest of each party to plan to keep his or her word if all others were to plan to keep their word and (ii) at every stage of the agreed course of actions, each party would believe that all others would keep their word. If the two conditions are met, a system of beliefs that the agreement will be kept would be self-confirming. Condition (ii) on its own would not do. Beliefs need to be justified. Condition (i) provides the justification. It offers the basis on which everyone could in principle believe that the agreement will be kept. A course of actions, one per party, satisfying condition (i) is called a Nash equilibrium, in honour of John Nash, who showed that the concept is not vacuous (Nash, 1950).3 Condition (i) on its own would not do either. It could be that it is in each agent’s interest to behave opportunistically if everyone believed that everyone else would behave opportunistically. In that case non-cooperation is also a Nash equilibrium, meaning that a set of mutual beliefs that the agreement will not be kept would also be self-confirming. Stated formally a Nash equilibrium is a set of strategies, one per agent, such that no agent would have any reason to deviate from his or her strategy if all the other agents were to pursue their respective strategies (Eq. (1)). Generally speaking, social games harbour multiple Nash equilibria. The empirical literature on institutions facilitating cooperation is gigantic. Prominent among them are studies of cooperative activity in small communities in poor countries. They include studies of reciprocity (credit, insurance, and labour effort), the construction of local public goods (village tanks, drainage structures, and flood protection), and the management of spatially confined common property resources (coastal fisheries, mangroves, grazing land, woodlands, and irrigation channels). Scholars studying cooperation in those activities have in large measure used the Prisoners’ Dilemma game as their theoretical tool-kit (see, e.g., Ostrom, 1990). They have evaluated communitarian institutions in terms of the ease with which people are able to escape the Dilemma. In fact neither the provision of local public goods nor the management of local common property resources (CPRs) involves the Prisoners’ Dilemma. In this paper I demonstrate that for CPRs and show why it matters. To be sure, people facing even a symmetric Prisoners’ Dilemma would be able to implement agreements where they share the benefits of cooperation unequally.4 But the Prisoners’ Dilemma has so strong a special structure that cooperation in the game cannot make anyone worse off than they would be if the parties were not to cooperate. In short, cooperation trumps non-cooperation for everyone in the game. Unfortunately, the latter cannot be guaranteed in social environments involving the provision of local public goods or the management of CPRs.5 It is shown below that in those games there are communitarian rewards

3 Condition (i), in the way I have phrased it, is called a ‘‘sub-game perfect (Nash) equilibrium’’, which is a natural extension of the concept of Nash equilibrium to inter-temporal games. See, for example, Osborne (2003). 4 That the benefits and burdens of managing CPRs are frequently distributed unequally, where the elite enjoy more of the benefits than the rest, has been well documented. See for example Baland et al. (2007). 5 Public goods games and CPR games in a timeless setting have similar structures. See Dasgupta and Heal (1979, Chapter 3).

and sanctions under which some members of a group are worse off than they would be if all parties acted non-cooperatively. ‘‘Exploitation’’ is the only word for characterizing such a state of affairs. But if the scholar visiting the site was to misread the social environment and interpret collective engagements as the community’s attempt to escape the Prisoners’ Dilemma, the field report he or she prepares would almost inevitably have a warm glow to it.6 Even if some members of the community suffered from exploitation, the scholar would not notice. That is because exploitation would be masquerading as cooperation. In this paper I build a model of CPRs to show how that can happen. The plan of the paper is as follows. In Section 3 Nash equilibrium strategies are distinguished from min–max strategies. The Prisoners’ Dilemma is reviewed next. We note there that in a Prisoners’ Dilemma, Nash equilibrium strategies are the same as min–max strategies. I next construct a timeless model of a CPR. It is shown that individual payoffs in a Nash equilibrium in the CPR game exceed min–max payoffs. This enables me to show that although the absence of cooperation leads to inefficiency, the CPR game is not a Prisoners’ Dilemma. In Section 4 the timeless model is assumed to be repeated indefinitely. Using an argument made familiar from the Folk Theorem in the theory of repeated games (Fudenberg and Maskin, 1986; Mailath and Samuelson, 2006), I show that cooperation can be exploitative. Section 5 concludes with some general observations.

3. Stage games We begin by considering a timeless game. Individuals are indexed by i. For simplicity of notation, I assume that the community consists of two individuals: i¼1 and 2. (The analysis that follows generalizes to any finite number of persons.) Let Si be the strategy set available to person i. In order to have a meaningful problem, we assume that Si contains more than one strategy. A strategy itself is denoted by si. Thus siASi. Person 1’s payoff function is denoted by p1(s1,s2), that of 2 by p2(s1,s2). Recall that a pair of strategies {s1*,s2*} is a Nash equilibrium of the game if

p1 ðs1 , s2 Þ Z p1 ðs1 , s2 Þ for all s1 A S1 and

p2 ðs1 , s2 Þ Z p2 ðs1 , s2 Þ for all s2 A S2

ð1Þ

Write

p1 ðs1 , s2 Þ ¼ p1 and p2 ðs1 , s2 Þ ¼ p2

ð2Þ

{p1*, p2*} is a pair of Nash equilibrium payoffs. The min–max payoffs for individuals 1 and 2, which we write as p1** and p2**, respectively, are defined as

p1 ¼ ½min s2 A S2

max

p1 ðs1 ,s2 Þ,

s1 A S1

and

p2 ¼ ½min s1 A S1

max s2 A S2

p2 ðs1 ,s2 Þ, ð3Þ

In words, Eq. (3) says that an individual’s min–max payoff is the payoff he or she is assured of no matter how malevolent the other person happens to be. Clearly

pi Z pi

ð4Þ

6 Empirical studies of cooperative arrangements are commonly written in a way that carries with it a warm glow. See, Feeny et al. (1990) and Bromley et al. (1992), among many others.



In what follows we study symmetric games only. That move simplifies the exposition greatly.

Table 1 Payoff matrix of the Prisoners’ Dilemma: d o a o b o g.

3.1. The Prisoners’ Dilemma

2

Table 1 depicts a 2-person game in normal form, in which each person’s strategy set consists of exactly two elements, x and y.7 If both individuals choose x, the payoff to each is a; if they both choose y, the payoff to each is b. But if 1 chooses y while 2 chooses x, the payoffs are d and g, respectively; whereas if 1 chooses x while 2 chooses y, the payoffs are g and d, respectively. Assume

doaobog

x

y

x

α,α

γ,δ

y

δ,γ

β,β

1

ð5Þ

The resulting game is a Prisoners’ Dilemma. In what sense is it a Prisoners’ Dilemma? To see the sense, notice that if inequalities (5) hold, x is the best strategy for person 1 no matter whether 2 chooses x or y. That means x is a dominant strategy for 1. Because the game is symmetric, x is the dominant strategy for 2 as well. So {x, x} is not only the unique Nash equilibrium pair of strategies, it is a dominant pair of strategies. But if the two were to choose y, the payoff to both would be higher. That is the dilemma. To summarize: the hallmark of the Prisoners’ Dilemma is that it has a unique, inefficient, dominant strategy Nash equilibrium. Notice that because x is the dominant strategy for both parties, a in Table 1 is not only the Nash equilibrium payoff for each party, it is also the min–max payoff. On returning to the notation of Eqs. (2) and (3), we record that particular feature of the Prisoners’ Dilemma as

pi ¼ pi , i ¼ 1,2

3

ð6Þ

Condition (6) is the reason why cooperation among a group of people facing the Prisoners’ Dilemma cannot be bad for any party. 3.2. Common property resource (CPR) In what follows the problem of the commons is illustrated by means of a formal model involving the use of a grazing land. The model is taken from Dasgupta and Heal (1979, Chapter 3). There are 2 herdsmen, indexed by i (i¼1 and 2). Cattle are private property. The pasture is neither privately owned nor state property, but is communally owned. Outsiders are not permitted to graze their cattle in the pasture, meaning that access to the land is not open to all: the grazing land is a CPR. The model is timeless. The size of the pasture is T. Cattle intermingle while grazing; so, on average the cows consume the same amount of grass. If X, a continuous variable, is the size of the herd in the pasture, total output (beef) is H(X, T), where H is taken to be linear-homogeneous of degree 1 in X and T. Assume H(0,T)¼0. Also assume that qH/qX 40 and qH/qT40, but that both partial derivatives diminish with increasing values of X and T, respectively. In short, I take H to be a production function in textbook economics. As T is fixed in size and H is linear-homogeneous of degree 1, we may eliminate T by writing H(X, T) ¼TH(X/T, 1), by setting T¼1 without loss of generality, and by defining F(X) H(X, 1). From the assumptions made on H, we may conclude that F(0)¼ 0; F0 (X)40; F00 (X)o0; and F(X)/X4F0 (X)40 for all XZ0.8 Fig. 1 depicts both F(X)/X (the average product of cattle) and F0 (X) (the marginal product of cattle). Assume that each herdsman is interested in his or her private profit. We normalize by choosing the market price of beef to be 1. 7 To relate to the general notation we have just developed, each of s1 and s2 is either x or y. 8 0 F (X) and F00 (X) are the first and second derivatives, respectively, of F.

Fig. 1

Let the market price of cattle be p (40). To have a problem worth studying (see Eq. (8)), I assume that F0 (0) 4p. 3.3. The unmanaged CPR We first determine the size of the herd that grazes on the CPR if the pair of cattle owners choose the size of their herds noncooperatively. Let xi be the size of i’s herd. For ease of computation, xi is assumed to be a continuous variable. Obviously, X¼ x1 þx2. Since cattle intermingle in the CPR, xiF(X)/X is i’s output of beef. Therefore i’s net profit, pi, is

pi ¼ xi FðXÞ=Xpxi , i ¼ 1,2

ð7Þ

As the CPR is unmanaged, we compute Nash equilibria of the noncooperative game. Because the model is symmetric, we search for a symmetric equilibrium. (It is easy to confirm that equilibrium is unique.) Consider herdsman i. If the size of the other person’s herd is x, Eq. (7) can be written as

pi ðxi , xÞ ¼ xi Fðxi þxÞ=ðxi þ xÞpxi

ð8Þ


4


Denote aggregate profit at the joint optimum by Po. Using Eq. (13) it follows that

Po ¼ FðX o ÞF 0 ðX o ÞX o 4 P 4 0

ð14Þ

o

In Fig. 1, P is the area of the rectangle JNRT. Condition (14) says that although profits are dissipated in the unmanaged CPR (Po 4 P*) because too many cattle graze on it, herdsmen do enjoy positive profits (p* 40). The problem of CPRs is not that profits are zero, but that they are not as high as they would be if the herdsmen cooperated. Although X*/2 is each individual’s herd size in equilibrium, it is not a dominant strategy. To confirm, notice that if either herdsman was to introduce a herd whose size is different from X*/2, the other herdsman would introduce a herd that does not number X*/2. Notice also from Eq. (8) that the min–max payoff for each herdsman is zero.9 Thus p 1 ¼ p2 ¼ 0:

ð15Þ

Comparing Eqs. (12) and (15) confirms that CPRs do not give rise to the Prisoners’ Dilemma. This is a fact I make use of in the following section.10

4. Long-term relationships: repeated interactions in the common

Fig. 2

Let xn be the size of each herd at a symmetric Nash equilibrium. By definition (recall Eq. (1)), xn is the value of xi that maximizes pi(xi, xn) in Eq. (8). Therefore, we differentiate pi(xi, xn) partially with respect to xi and equate the differential coefficient to zero. That yields Fðxi þx Þ=ðxi þ x Þ þ xi F 0 ðxi þ x Þ=ðxi þ x Þxi Fðxi þ x Þ=ðxi þ x Þ2 ¼ p ð9Þ n

At a symmetric Nash equilibrium, xi in Eq. (9) equals x . We now re-arrange terms to confirm that the aggregate herd size in the unmanaged CPR, which we write as X*, satisfies FðX Þ=X þ F 0 ðX Þ ¼ 2p,

X ¼ 2x

ð10Þ

Now use Eq. (10) to confirm that aggregate profit, (F(X*) pX*), which we write as P*, can be expressed as

P ¼ ½FðX ÞX F 0 ðX Þ=2 4 0

ð11Þ

Eq. (11) says that both herdsmen earn positive profits. In Fig. 1,

P* is the area of the rectangle JKLM. From Eq. (11) it follows that profit per herdsman is

P =2 ¼ ½FðX ÞX F 0 ðX Þ=4 4 0

ð12Þ

In Fig. 2, the Nash equilibrium pair of profits {P*/2, P*/2} is the point A. The unmanaged CPR should be unattractive to the herdsmen because they could increase their profits by cooperating. What would be a reasonable agreement among the herdsmen? As the model is symmetric, imagine that the pair agree to maximize aggregate profit and share the profit equally. If X is the size of the herds, aggregate profit is F(X) pX. Maximizing this yields the condition F 0 ðX Þ ¼ p:

Suppose the pair expect to face the same CPR problem year after year. By ‘‘expect’’, we mean that no matter how many years into the future they peer at, the herdsmen believe there is a chance they will face the same CPR problem even beyond that year. We assume also that, living as they do in proximity, the size of each herd is recorded by both every year (but see footnote 13 for a relaxation of the assumption). Also imagine that the parties are not able to depend on the law of contracts because the nearest courts are far from their residence. There may even be no lawyer in sight. In rural parts of sub-Saharan Africa, for example, much economic life is shaped outside a formal legal system. Even though no external enforcer may be available, people there do transact. But why should the parties be sanguine that agreements will not turn sour because of opportunism? Returning to our previous example, why should the herdsmen trust one another to comply with an agreement that says each is to limit his herd size to Xo/2 in every period? 4.1. Social norms They would be sanguine if agreements were mutually enforced. The general idea is this: a credible threat by each that stiff sanctions would be imposed on anyone who broke an agreement would deter everyone from breaking it.11 The problem then

9 This is simple to confirm. If, say, herder 2 was to flood the commons with cattle, say, to the point where F(x2)/x2 ¼p, the best that herder 1 could do would be to stay out of the commons. His profit would then be zero. 10 If the number of herdsmen is large, the unmanaged CPR approximates an open-access resource. To confirm, suppose N is the number of herdsmen. It is simple to verify (Dasgupta and Heal, 1979, Chapter 3) that if N was large, Eq. (10) would be

ð13Þ

Eq. (13) says that the optimum herd size is one at which the marginal product of cattle equals their price. It is a well known result in economic theory. Let Xo be the solution of Eq. (13). Comparing Eqs. (10) and (13), we find that X* 4Xo (Fig. 1). We conclude that there are too many cattle in the unmanaged CPR.

FðX Þ=X p: The (approximate) equation says that profits are dissipated almost entirely at the open-access equilibrium. That case was studied by Gordon (1954) in a classic article. Hardin’s famous metaphor, the ‘‘tragedy of the commons’’ (Hardin, 1968) was about open-access CPRs. 11 The corresponding mechanism in evolutionary biology is reciprocal altruism (Trivers, 1971).



is to make the threat of stiff sanctions credible. Here, we interpret sanctions as withdrawal of future cooperation from anyone who breaks the agreement. The solution to the credibility problem in this case is achieved by recourse to social norms of behaviour. Even the colloquial usage of the term ‘‘social norm’’ carries with it the thought that the parties expect to interact with one another directly or indirectly over time. That is why mutual enforcement of collective agreements has been studied frequently in the context of long-term relationship among people.12 Although norms have been found to evolve, we study them here as though they can be called upon and instituted when and where a community finds it useful. The advantage of the analytical approach to the study of social norms, as opposed to a historical approach, is that it enables us to identify those particular characteristics of rules of behaviour that can be deemed to be social norms. In what follows we assume that behaviour by each party is observable by all parties. It follows that social norms can include sanctions that are to be imposed on those who break agreements without due cause.13 By a ‘‘social norm’’ we mean a rule of behaviour followed by all members of a community. Norms are of the form, ‘‘If someone possesses characteristics M (a Brahmin), he should do w if P occurs; but should do x otherwise; whereas if someone possesses characteristics N (a Sudra), she should do y if Q occurs; but should do z otherwise’’. For a rule of behaviour to be a social norm, however, it must be the case that it is in the interest of each party to act in accordance with the rule if all others were to act in accordance with it, which is to say that for a rule of behaviour to be a social norm, it must be a Nash equilibrium. (If a rule of behaviour is not a Nash equilibrium, it would be in someone’s interest to violate the rule.)

4.2. Cooperation for mutual benefit: equality How may the idea of social norms be applied to groups wishing to cooperate over the use of CPRs? To answer, we return to the model of the two herdsmen and assume that the CPR game is expected to be repeated over and over again. Time is discrete and is denoted by t( ¼0,1,2,y). We now call the CPR game studied in Section 3 the stage game, and the indefinite repetition of the stage game the repeated game. I assume that the herdsmen discount their future profits at the constant rate, r(40). I assume also that r is ‘‘small’’, a notion that will be made precise below. Imagine that at t ¼0 the herdsmen agree to limit each of their herds to Xo/2 cattle for all t, where Xo is the optimum herd size (Eq. (13)). Under their agreement, each herdsman’s profit in each period is Po/2 (Eq. (14)). The problem facing the herdsmen is to enforce their agreement. Consider the following strategy for each herdsman: Begin by introducing Xo/2 cattle into the pasture and continue to graze Xo/2 so long as neither herdsman has broken the agreement; but introduce X*/2 cattle into the pasture each year following the first violation of the agreement by someone. Game theorists have

12 Mailath and Samuelson (2006) contains the definitive treatment of the problem. 13 The requirement that actions are observable can be weakened. Suppose transgressors are able to avoid detection with a small probability. The social norm would still require that known transgressors be punished. Provided it was possible for parties to inflict a sufficiently heavy punishment on transgressors when their transgressions were observed, no one would transgress. It would serve no purpose in this paper to include extensions involving imperfect monitoring. So I assume that actions are mutually observable. Mailath and Samuelson (2006) have an extensive discussion of long-term relationships under imperfect monitoring.

5

christened the strategy the ‘‘grim strategy’’, or simply grim, because of its unforgiving nature.14 Let us see how grim would work. The repeated game begins at t¼ 0. Without loss of generality, consider herdsman 1. Suppose herdsman 2 has chosen grim and both know that he has done so. Herdsman 1 now wonders whether it will ever be in his interest to break the agreement. He realizes however, that if it would ever be in his interest to break the agreement, it would be in his interest to do so at t¼ 0. And because 1 knows that 2 has chosen grim, he knows 2 will introduce Xo/2 cattle into the CPR at t ¼0. Let g be the maximum (one period) gain in profit at t ¼0 that herdsman 1 could enjoy by breaking the agreement.15 Obviously, g40, which is after all why he is wondering whether to break the agreement. But he knows that if he were to break the agreement at t ¼0, herdsman 2 will introduce X*/2 cattle into the CPR from t¼ 1 onward. Herdsman 1 also knows that because 2 will increase his herd to X*/2 from t¼1 onward, he himself will find it in his own best interest to introduce X*/2 cattle into the CPR from t ¼1 (remember, X*/2 is a Nash equilibrium of the stage game). But if both switch permanently to X*/2 from t¼ 1, herdsman 1’s profit flow will be p*. So, 1’s choices amount to (i) cooperate so long as the game lasts, and (ii) break the agreement at t¼ 0. Under (i), his profit stream would be po[1þ(1þr) 1 þ(1þr) 2)þ?]; whereas, under (ii) it would be {gþ po þ p*[(1 þr) 1 þ (1þ r) 2 þ?]}. It follows that herdsman 1 will not find it to his advantage to break the agreement if16 r oðpo p Þ=g:

ð16Þ

We have proved that if inequality (16) holds and herdsman 2 is known to have chosen grim, herdsman 1 cannot do better than to choose grim himself. So, if inequality (16) holds, the strategy pair {grim, grim} is a Nash equilibrium of the repeated game. In equilibrium, neither herdsman behaves opportunistically, so sanctions do not have to be applied ever. The above argument also proves that if r 4(po p*)/g, cooperation by means of grim is impossible. But one can say something a lot stronger: it is not possible to enforce cooperation by means of any social norm (grim or otherwise) if r 4(po p*)/g.17 Notice the interesting way the productivity of the CPR enters the picture. Inequality (16) says that if (po p*)/g is small, cooperation is possible only if r is correspondingly small, other things being equal. Sadly, even when cooperation is possible (e.g., by means of the grim social norm), non-cooperation is also a possible equilibrium outcome. If each herdsman was to believe that the other would break the agreement from the start, both would break the agreement from the start. Non-cooperation would involve each herdsman selecting the strategy, ‘‘choose X*/2 at all times’’. Failure to cooperate could be simply due to a collection of unfortunate, self-confirming beliefs, nothing more (see below). 4.3. Cooperation for mutual benefit: inequality Entitlements to the products from CPRs are frequently based on private holdings of other assets. Cavendish (2000) has reported that in absolute terms, richer households in his sample of villages in Zimbabwe took more from CPRs than poor households. In her 14 Mailath and Samuelson (2006, p. 52) contrasts ‘‘grim’’ with what they call ‘‘Nash-reversion’’. 15 Thus, g¼maxx [xF(xþ xo)/(xþxo) px] po. If 1 is to enjoy the gain g, the size of his herd would be arg maxx [xF(xþxo)/(xþ xo)–px]. The number exceeds X*/2. 16 It is easy to prove that if the number of herdsmen is N(Z 2), the necessary condition for cooperation in long-term relationships is ro (po–p*)/g. See Dasgupta (2008). 17 The way to prove that is to note that of all possible strategies, grim inflicts the maximum punishment for a single misdemeanour.


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work on coastal fisheries and forests products, McKean (1992) noted that benefits from CPRs are frequently captured by the elite. Agarwal and Narain (1996) exposed the same phenomenon in their study of water management in the Gangetic plain. The exclusion of women has also been recorded. Molians (1998), for example, has recorded the way gender inequalities are woven into local collective action in poor countries. Our model of the CPR game is symmetric. How could inequality arise there? The answer is that the herdsmen also have a life outside the CPR. Even though the model sees the herdsmen, qua herdsmen, to be equally placed on the grazing land, it could be that the pair are of unequal status in their community, say, because one is richer than the other. It could then be that their unequal status translates itself into an agreement in which one of them is permitted to herd more cattle than the other. We can now apply the argument deployed in Section 4.2 to show that, so long as both herdsmen gain from cooperation, an unequal sharing of the benefits from the CPR can be sustained by the use of grim if r is small enough. Consider an agreement at t ¼0 that says that in each period, person 1’s herd must not exceed aXo and person 2’s herd must not exceed (1 a)Xo, where 14a 41/2 and (1 a)Po 4 P*/2. If the agreement was kept, the herdsmen’s profits in each period would be aPo and (1 a)Po, respectively. Under the agreement, herdsman 2 earns less than herdsman 1 (a 41/2), but more than what he would earn if the CPR was unmanaged ((1–a)Po 4 P*/2). So, even though the agreement is to share the benefits of cooperation unequally, both parties gain from cooperation. In Fig. 2, C denotes the pair of profits earned by the herdsmen each year under the agreement, that is, C is the point {aPo, (1 a)Po}. As C lies to the northeast of A, a repetition of our previous argument shows that, provided r is sufficiently small (it has to be less than upper limit in inequality (16)), grim can serve as a social norm for enforcing C every year. 4.4. Breakdown of cooperation It is instructive to apply the insights from the repeated CPR game to wider contexts. We have confirmed that if r were large, cooperation would not be possible: short term opportunism would prove to be too tempting. Let us now interpret r to be the hazard rate associated with the possibility that the CPR game will cease at some future date. Under this interpretation r is the probability that the pair will not meet next year conditional on having met this year. The present discounted value of the flow of profits from the CPR, be it managed or unmanaged, should now be interpreted as the ‘‘expected value’’ of the flow of profits. We now have a tool to explain how a community where members have been cooperating in the past, can skid to a state of affairs where the parties cease to cooperate. Ecological stress (caused, for example, by high population growth and prolonged droughts) often leads people to fight over land and natural resources (Homer-Dixon, 1999; Diamond, 2005). More generally, political instability (in the extreme, civil war) would be a reason why people discount the future benefits of cooperation at a high rate, if for no other reason than a heightened fear that their community will not survive in its present shape. For whatever reason, if discount rates were to increase sufficiently relative to the parameters characterizing the social environment, cooperation would cease. Social norms work only when people have reasons to value the future benefits of cooperation. Cooperation would also cease if, other things being equal, g rose (inequality (16)) or if population grew (footnote 16). Contemporary examples illustrate all those possibilities. Local institutions have been observed to deteriorate in the unsettled regions of sub-Saharan Africa (see, e.g., Lopez, 1998). Communal

management systems that once protected Sahelian forests from unsustainable use were destroyed by governments keen to establish their authority over rural people. But Sahelian officials had no expertise at forestry, nor did they have the resources to observe who took what from the forests. Many were corrupt. Rural communities were unable to switch from communal governance based on social norms to governance based on the law: the former was destroyed and the latter did not really get going. The collective vacuum has had a terrible impact on people whose lives had been built round their forests and woodlands. Reviewing her findings on small irrigation systems in Nepal, Ostrom (1992, 1996) reported the breakdown of cooperation among farmers in several instances and she identified the causes that ranged from imperfect monitoring of water use to wellmeaning but misdirected aid from international organizations. In a study of a sample of villages in southern India, Balasubramanian (2008) has reported that village tanks have deteriorated over the years owing to a decline in collective investment in their maintenance. This decline has taken place as richer households have invested increasingly in private wells. As poor households depend not only on the tank water but also on the fuelwood and fodder that grow round the tanks, construction of private wells has accentuated economic stress among the poor.18 In each of the above studies, the breakdown of cooperation could be interpreted in terms of a rise in r (inequality (16)), or an increase in g (inequality (16)), or an increase in population (footnote 16). Ominously, there are subtler pathways by which societies can tip from a state of mutual trust to one of mutual distrust. When r is low, both cooperation and non-cooperation are equilibrium outcomes. So, a society could tip over from cooperation to noncooperation simply because of a change in beliefs. The tipping may have nothing to do with any discernable change in circumstances; the entire shift in behaviour could be triggered in people’s minds. The switch could occur quickly and unexpectedly, which is why it would be impossible to predict and why it would cause surprise and dismay. People who woke up in the morning as friends would discover at noon that they are at war with one another. Of course, in practice there are usually cues to be found. False rumours and propaganda create pathways by which people’s beliefs can so alter that they tip a society where people trust one another to one where they do not. The reverse can happen too, but it takes a lot longer. Rebuilding a community that was previously racked by civil strife involves building trust. Non-cooperation does not require as much coordination as cooperation does. Not to cooperate usually means to withdraw. To cooperate, people must not only trust one another to do so, they must also coordinate on a social norm that everyone understands. That is why it’s a lot easier to destroy a society than to build it.19 4.5. Exploitation as cooperation Is it possible that someone is worse off in a long-term relationship than he would have been if he had not embarked on the relationship? In other words, can long-term relationships involve exploitation? Empirical studies of communitarian institutions have not investigated that possibility, perhaps for reasons mentioned in our discussion of the Prisoners’ Dilemma (Section 4.1). 18 Ghate et al. (2008), which contains the paper by Balasubramanian, is an excellent collection of empirical studies from South Asia that narrate the breakdown of cooperation in CPRs. 19 For a discussion of these dark matters in the wider context of ‘‘social capital’’, see Dasgupta (2000, 2008, 2009, 2010).



To explore the possibility, let us return to our herdsmen. Consider an agreement at t ¼0 that says that each year person 1’s herd must not exceed bXo and person 2’s herd must not exceed (1 b)Xo cattle, where b is a number such that [F(X*) pX*]/ 24(1 b)[F(Xo) pXo]40. If the agreement were kept, the herdsmen’s profits each year would be bPo and (1 b)Po, respectively. Under the agreement, herdsman 2 would not only earn less than herdsman 1, but also earn less than he would if the CPR was unmanaged. In Fig. 2, D is the pair of profits {bPo, (1 b)Po}. Observe that D is to the southeast of A. So the question arises: can D be enforced in a long-term relationship? Notice that grim cannot be deployed for the purpose in hand. The reason is that (1 b)Po o P*/2. That means reverting to the Nash equilibrium strategy of the stage game would not be a deterrent for herdsman 2. So some other social norm has to be devised. Notice also that (1 b)Po 4 p**¼0, which says herdsman 2’s annual profit under the agreement exceeds his min–max value. So p** can be used as the anchor on which to construct a social norm. The problem is, {p**, p**} is not a Nash equilibrium pair of profits of the stage game. That is why the required social norm is a lot more complicated than grim. Call a person a conformist if he cooperates with those who are conformists but punishes those who are non-conformists. The definition sounds circular, but it is not, because we now assume that the social norm we are trying to construct requires that at t ¼0, a person should keep the promise he has made. It would then be possible for anyone in any period to determine who is a conformist and who is not. For example, if someone were ever to break the original agreement (which is that herdsman 1 is limited to bXo cattle, while herdsman 2 is limited to (1 b)Xo cattle), he would be judged to be a non-conformist. The social norm we seek would require that the non-conformist be pushed to his min–max payoff for a sufficiently large number of years so as to make him feel the pain. But pushing someone to his min–max payoff can be very costly to those who impose the punishment. The trick is to have the social norm require that the punishment of being ‘‘min– maxed’’ be inflicted not only upon those in violation of the original agreement (first-order violation), but also upon those who fail to punish those in violation of the agreement (secondorder violation); upon those who fail to punish those who fail to punish those in violation of the agreement (third-order violation), and so on, indefinitely. If r is sufficiently small, increasingly longer periods of punishment for, respectively, first-order, second-order, and higher-order violations can be incorporated in the social norm in such a manner that it would not be in the interest of either herdsmen ever to be a non-conformist. When the numbers of periods (for first-order, second-order, and higher-order violations) are so chosen, the strategy can serve as a social norm, meaning that it is in the self interest of each herdsmen to accept the norm if the other accepts it. Exploitation of herdsmen 2 by herdsman 1 is the only way to characterize the shares in D.20 All traditional societies appear to have sanctions in place for firstorder violations. The sanctions against higher-order violations have not been documented much may be because they are not needed to be built into social norms if it is commonly recognized that people

20 I have chosen D (a point where aggregate profit is at a maximum) as the agreement point only because my purpose here has been to show that exploitation can masquerade as cooperation, nothing more. In fact, any pair of payoffs that is the northeast of {0, 0}, such as the point E in Fig. 2, can be supported under longterm relationships, provided r is sufficiently small. The latter finding is known as the Folk Theorem in game theory. Mailath and Samuelson (2006) provides a detailed account of the theory of the Folk Theorem. Proof of the version of repeated games I am invoking in the text is in Mailath and Samuelson (2006, p. 77).

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feel an emotional urge to punish those who have broken agreements. Anger facilitates cooperation by making the threat of retaliation that much more credible.21

5. Commentary Cooperation does not require long-term relationships. So long as people are connected to one another, directly or indirectly, and not necessarily via the same cooperative venture, an argument identical to the one we have recounted here can be deployed to account for cooperation among people who may not even know one another (e.g, the social norm could have it that person 1 is to punish person 2 by ceasing to cooperate in a venture they have undertaken if 2 was to renege on an agreement between him and person 3 involving a different venture, and so on, either back to person 1 or indefinitely along a chain involving new participants with the passage of time). The reach of the argument deployed in Sections 2 and 3 is enormous.22 Social norms are not constructed out of thin air; they evolve. People are embedded in them from birth, a feature that enables the generations to cooperate and help contemporaries to cooperate. The inheritance of debt in poor societies is an instance of that. However, the analytical approach we have taken here, common in the theory of games, enables us to better understand the logic of cooperation in the world we have come to know. Empirical studies of long-term relationships over common property resources have often had a warm glow about them. That relationships matter for a person’s well-being is no doubt a trite observation, but people writing on communitarian institutions have wanted to claim more. In countries where the law does not function well, where officials regard the public sphere to be their private domain, where impersonal markets are often absent, communitarian relationships are what keeps people alive, if not well. That explains their attraction. But we need to bear counterfactuals in mind. It could be that communitarian relationships prevent impersonal transactions from taking place. Moreover, it may be that personal obligations inherited from the past prevent public officials from acting dispassionately. What appears as corruption in the North could well be a reflection of cooperation in the South. Inequity per se is not an evidence of exploitation. That is one reason why it will prove extremely hard to detect exploitation even if it is present. Moreover, identifying exploitation involves a study of counter-factuals, involving the question: What would the allocation of resources be if the parties were not engaged in a long-term relationship? That makes identifying exploitation harder still. It was suggested to me at a lecture where I spoke on exploitation that the social norm studied in Section 4.5 involves ‘‘coercion’’, not cooperation. There is truth in that, but then all cooperation requires coercion. Even in ideal democracies, 21 However, on a riverboat ride in Kakadu National Park, Australia, in the summer of 2004, my wife and I were informed by the guide, a young aborigine, that his tribe traditionally practised a form of punishment that involved spearing the thigh muscle of the errant party. When I asked him what would happen if the party obliged to spear an errant party were to balk at doing so, the young man’s reply was that he in turn would have been speared. When I asked him what would happen if the person obliged to spear the latter miscreant were to balk, he replied that he too would have been speared! I asked him if the chain he was describing would go on indefinitely Our guide said he did not know what I meant by ‘‘indefinitely’’, but as far as he knew, there was no end to the chain. 22 Greif et al. (1994) and Greif (2005) contain studies of cooperation among Medieval traders. They have unearthed records where sanctions involving the withdrawal of cooperation for breach of agreement are explicitly mentioned. See Mailath and Samuelson (2006) for a comprehensive set of extensions of the theory driving the analysis in Sections 3 and 4, including a study of cooperation with imperfect monitoring among the players.


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citizens are imagined to endow the State with coercive powers so as to carry out its functions. In any event, because all social interactions in our world are embedded in a mesh of tied agreements, it could be that a person gains from cooperation in one venture even while she finds herself being exploited in another venture. As the agreements are held together by an interconnected set of their own bootstraps, she is unable to disengage herself from the venture in which she is exploited for fear of the consquences. Ethnographic studies can be suggestive of exploitation. Inequities in patron–client relationships are known to take such forms as to make it likely that the ‘‘client’’ is worse off in consequence of the relationship than he would have been in its absence. Among contemporary societies, there are many where women remain socially inferior beings, prevented from inheriting assets, obtaining education, and entering choice occupations, all of which excludes them in turn from credit, saving, and insurance markets. But such people would appear to accept the restrictions in their lives as a matter of course, without visible or audible complaint. The analysis of long-term relationships in Section 4.5 is suggestive of why. References Agarwal, A., Narain, S., 1996. Dying Wisdom: Rise, Fall and Potential of India’s Traditional Water Harvesting Systems. Centre for Science and Development, New Delhi. Baland, J.-M., Platteau, J.-P., 1996. Halting Degradation of Natural Resources: Is there a Role for Rural Communities? Clarendon Press, Oxford. Baland, J.-M., Bardhan, P., Bowles, S. (Eds.), 2007. Inequality, Cooperation, and Environmental Sustainability. Russell Sage Foundation, New York. Balasubramanian, R., 2008. Community tanks vs private wells: coping strategies and sustainability issues in South India. In: Ghate, R., Jodha, N.S., Mukhopadhyay, P. (Eds.), Promise, Trust and Evolution: Managing the Commons of South Asia. Oxford University Press, Oxford. Binmore, K., Dasgupta, P., 1987. The Economics of Bargaining. Basil Blackwell, Oxford. Bromley, D.W., et al. (Eds.), 1992. Making the Commons Work: Theory, Practice and Policy. ICS Press, San Francisco. Cavendish, W., 2000. Empirical regularities in the poverty–environment relationships of rural households: evidence from Zimbabwe. World Development 28 (11), 1979–2003. Dasgupta, P., 2000. Economic progress and the idea of social capital. In: Dasgupta, P., Serageldin, I. (Eds.), Social Capital: A Multifaceted Perspective. World Bank, Washington, DC, pp. 325–424. Dasgupta, P., 2008. Common property resources: economic analytics. In: Ghate, R., Jodha, N., Mukhopadhyay, P. (Eds.), Promise, Trust, and Evolution: Managing the Commons of South Asia. Oxford University Press, Oxford. Dasgupta, P., 2009. Trust and cooperation among economic agents. Philosophical Transactions of the Royal Society B 364 (1533), 3301–3309.

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