Appropriating the Commons: A Theoretical Explanation

*Armin Falk, Ernst Fehr, and Urs Fischbacher*

In his classic account of social dilemma situations, Hardin (1968) develops his pessimistic view of the “tragedy of the commons.” Given the incentive structure of social dilemmas, he predicts inefficient excess appropriation of common-pool resources. Hardin’s view has been challenged by the insights of numerous field studies reported in the seminal book by Ostrom (1990). In this book the metaphor of a tragedy is replaced by the emphasis that people are able to govern the commons. Ostrom shows that in many situations people are able to cooperate and improve their joint outcomes. Moreover, the reported field studies point to the importance of behavioral factors, institutions, and motivations. However, although it has been shown that these factors collectively influence behavior, it is of course nearly impossible to isolate the impact of individual factors.

This is why we need controlled laboratory experiments: Only in an experiment is it possible to study the role of each factor in isolation. In carefully varying the institutional environment, the experimenter is able to disentangle the importance of different institutions and motivations. The regularities discovered in the lab then can be used to better understand the behavior in the field. In this paper we concentrate on three such empirical regularities, which are reported in Walker et al., (1990), and Ostrom et al. (1992).^{1} They first study a baseline situation that captures the central feature of all common-pool resource problems: Because of negative externalities, individually rational decisions and socially optimal outcomes do not coincide. In a next step, the baseline treatment is enriched with two institutional features, the possibility of informal sanctions and the possibility to communicate. The empirical findings can be summarized as follows: In the baseline common-pool resource experiment, aggregate behavior is best described by the Nash equilibrium of selfish money maximizers. People excessively appro-

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5
Appropriating the Commons: A Theoretical Explanation
Armin Falk, Ernst Fehr, and Urs Fischbacher
In his classic account of social dilemma situations, Hardin (1968) develops his pessimistic view of the “tragedy of the commons.” Given the incentive structure of social dilemmas, he predicts inefficient excess appropriation of common-pool resources. Hardin’s view has been challenged by the insights of numerous field studies reported in the seminal book by Ostrom (1990). In this book the metaphor of a tragedy is replaced by the emphasis that people are able to govern the commons. Ostrom shows that in many situations people are able to cooperate and improve their joint outcomes. Moreover, the reported field studies point to the importance of behavioral factors, institutions, and motivations. However, although it has been shown that these factors collectively influence behavior, it is of course nearly impossible to isolate the impact of individual factors.
This is why we need controlled laboratory experiments: Only in an experiment is it possible to study the role of each factor in isolation. In carefully varying the institutional environment, the experimenter is able to disentangle the importance of different institutions and motivations. The regularities discovered in the lab then can be used to better understand the behavior in the field. In this paper we concentrate on three such empirical regularities, which are reported in Walker et al., (1990), and Ostrom et al. (1992).1 They first study a baseline situation that captures the central feature of all common-pool resource problems: Because of negative externalities, individually rational decisions and socially optimal outcomes do not coincide. In a next step, the baseline treatment is enriched with two institutional features, the possibility of informal sanctions and the possibility to communicate. The empirical findings can be summarized as follows: In the baseline common-pool resource experiment, aggregate behavior is best described by the Nash equilibrium of selfish money maximizers. People excessively appro-

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priate the common-pool resource and thereby give rise to the “tragedy” predicted by Hardin (1968). Giving subjects the possibility to sanction each other, however, strongly improves the prospects for cooperative behavior. The reason is that many people sanction defectors. This is surprising because sanctioning is costly and therefore not consistent with the assumptions that provide the basis for Hardin’s pessimistic view, that is, that subjects are selfish and rational. A similar observation holds for the communication environment. Allowing for communication also increases cooperative behavior. The resulting efficiency improvement is again inconsistent with the behavioral assumptions underlying Hardin’s analysis because communication does not alter the material incentives.
Taken together, therefore, we have the following puzzle: In a sparse institutional environment, people tend to overharvest common-pool resources. In this sense the pessimistic predictions by Gordon (1954) and Hardin (1968), which are based on the assumptions of selfish preferences, are supported. At the same time, however, we find the efficiency-enhancing effect of informal sanctions and communication. This is in clear contradiction to the standard rational choice view, because why should a rational and selfish individual sacrifice money in order to sanction the behavior of another subject? And why should a money-maximizing subject reduce his or her appropriation level following some cheap talk? The question is more general: Why is the rational choice conception correct in one setting and wrong in another?
In this paper we suggest an integrated theoretical framework that is capable of explaining this puzzle. We argue that the reported regularities are compatible with a model of human behavior that extends the standard rational choice approach and incorporates preferences for reciprocity and equity. The basic behavioral principle that is formalized in our model is that a substantial fraction of the subjects act conditionally on what other subjects do. If others are nice or cooperative, they act cooperatively as well, but if others are hostile, they retaliate.2 Our model also accounts for the fact that there are selfish subjects who behave in the way predicted by standard rational choice theory. We formally show that the interaction of these two diverse motivations (reciprocity and selfishness) and the institutional setup is responsible for the observed experimental outcomes. In the absence of an institution that externally enforces efficient appropriation levels, the selfish players are pivotal for the aggregate outcome. However, if there is an institutional setup that enables people to impose informal sanctions or allows for communication, the reciprocal subjects discipline selfish players and thus shape the aggregate outcome. Moreover, our model shows that when the members of a group have a preference for reciprocity or equity, the common-pool resource problem is transformed into a coordination game with efficient and inefficient equilibria. If subjects are given the opportunity to communicate, they can, therefore, ensure that the equilibrium with the efficient appropriation level is reached.
In the presence of a preference for reciprocity and equity, communication is a coordination device that helps subjects to coordinate their behavior on the low—

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appropriation equilibrium. Thus, if the institutional setup allows for sanctions or for communication, there is less appropriation in common-pool resource problems and higher voluntary contributions in public goods situations. Even though it is our main purpose in this chapter to show that the approach is able to account for the seemingly contradictory evidence of common-pool resource experiments, we believe the developed arguments are very general and likely to extend beyond the lab.
In the next section, we briefly outline the basic structure of our approach and recently developed fairness models. Then we apply our model to the standard common-pool resource game and discuss the theoretical predictions in light of empirical findings. We also provide propositions for a common-pool resource game with sanctioning opportunities as well as a discussion on the role of communication in the presence of reciprocal preferences. The subsequent section contains a comparison of common-pool resource results to those arrived in public goods games. The final section provides the conclusion.
THEORETICAL MODELS OF RECIPROCITY AND FAIRNESS
A large body of evidence indicates that fairness and reciprocity are powerful determinants of human behavior (for an overview, see e.g., Fehr and Gächter, 2000b). As a response to this evidence, various theories of reciprocity and fairness have been developed (Rabin, 1993; Levine, 1998; Bolton and Ockenfels, 2000; Fehr and Schmidt, 1999; Falk and Fischbacher, 1999; Dufwenberg and Kirchsteiger, 1998; Charness and Rabin, 2000). These models assume that—in addition to their material self-interest—people also have a concern for fair outcomes or fair treatments. The impressive feature of several of these models is that they are capable of correctly predicting experimental outcomes in a wide variety of experimental games. Common to all of these models is the premise that the players’ utility depends not only on their own payoff but also on the payoff(s) of the other player(s). This assumption stands in sharp contrast to the standard economic model according to which subjects’ utility is based solely on their own absolute payoff.
Some of the models mentioned are based on the notion that people care for fair outcomes (Bolton and Ockenfels, 2000; Fehr and Schmidt, 1999). Other models are based on the assumption that people evaluate the fairness of others’ action in terms of the kindness of the intentions that triggered the action (Rabin, 1993; Dufwenberg and Kirchsteiger, 1999). Intention-based fairness models capture an important aspect of what has been called procedural fairness by some authors (e.g., Lind and Tyler, 1988). A third class of models combines outcome-based and intention-based notions of fairness (Falk and Fischbacher, 1998; Charness and Rabin, 2000). The experimental evidence (see, e.g., Blount, 1995; Falk et al., 2000a) indicates that subjects do not only sanction because they want to achieve fair outcomes but that the motive to punish unfair intentions is also a major deter-

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minant of sanctioning behavior. Therefore, approaches that rely on distributional concerns and on rewarding and sanctioning of intentions (as, e.g., in Falk and Fischbacher, 1998) best capture the experimental regularities.
All mentioned fairness theories are rational choice theories in the sense that they allow for interdependent preferences but assume rational individuals. This assumption may be criticized because often people act not fully rational but boundedly rational (e.g., Selten, 1998; Dietz and Stern, 1995). Although we are generally sympathetic with this view, we would like to point out that so far there is no formal model of bounded rationality that is able to predict the experimental results presented in this chapter in a rigorous way.
In the games analyzed in this chapter, the Falk and Fischbacher model and the Fehr and Schmidt model yield similar predictions. We therefore restrict our attention to the latter model because it is relatively easy to apply in our context. The Bolton and Ockenfels model also yields similar predictions in the baseline common-pool resource environment, but predicts a wrong punishment pattern in the common-pool resource game with punishment opportunities. The reason is that in their model, each player does not evaluate fairness toward each other player (as in the Falk and Fischbacher and the Fehr and Schmidt models), but rather toward the group average. This basically means that people are indifferent between punishing defectors or punishing cooperators, a prediction that is at odds with the experimental data. Finally, the Dufwenberg and Kirchsteiger model and the Charness and Rabin model are extremely complicated and often do not generate precise predictions. Both models often predict many equilibria. Finally, we do not apply altruism models (see, e.g., Palfrey and Prisbrey, 1997) because these models are not compatible with sanctions, nor with the fact that people cooperate conditionally.
In the Fehr and Schmidt model, fairness is modeled as “inequity aversion.” An individual is inequity averse if he or she dislikes outcomes that are perceived as inequitable. This definition raises, of course, the difficult question of how individuals measure or perceive the fairness of outcomes. Fairness judgments inevitably are based on a kind of neutral reference outcome. The reference outcome that is used to evaluate a given situation is itself the product of complicated social comparison processes. In social psychology (Adams, 1963; Festinger, 1954; Homans, 1961) and sociology (Davis, 1959; Pollis, 1968; Runciman, 1966), the relevance of social comparison processes has been emphasized for a long time. One key insight of this literature is that relative material payoffs affect people’s well-being and behavior. As we will see, without the assumption that relative payoffs matter at least to some people, it is difficult, if not impossible, to make sense of the empirical regularities observed in common-pool resource experiments. There is, moreover, direct empirical evidence suggesting the importance of relative payoffs. The results in Agell and Lundborg (1995) and Bewley (1998), for example, indicate that relative payoff considerations constitute an important constraint for the internal wage structure of firms. In addition, Clark and Oswald

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(1996) show that comparison incomes have a significant impact on overall job satisfaction. Strong evidence for the importance of relative payoffs also is provided by Loewenstein et al. (1989). These authors asked subjects to ordinally rank outcomes that differ in the distribution of payoffs between the subject and a comparison person. On the basis of these ordinal rankings, the authors estimate how relative material payoffs enter the person’s utility function. The results show that subjects exhibit a strong and robust aversion against disadvantageous inequality: For a given own income xi subjects rank outcomes in which a comparison person earns more than xi substantially lower than an outcome with equal material payoffs. Many subjects also exhibit an aversion against advantageous inequality, although this effect seems to be significantly weaker than the aversion against disadvantageous inequality.
The determination of the relevant reference group and the relevant reference outcome for a given class of individuals ultimately is an empirical question. The social context, the saliency of particular agents, and the social proximity among individuals are all likely to influence reference groups and outcomes.3 Because in the following discussion we restrict attention to individual behavior in economic experiments, we have to make assumptions about reference groups and outcomes that are likely to prevail in this context. In the laboratory it is usually much simpler to define what is perceived as an equitable allocation by the subjects. The subjects enter the laboratory as equals, they don’t know anything about each other, and they are allocated to different roles in the experiment at random. Thus, it is natural to assume that the reference group is simply the set of subjects playing against each other and that the reference point, that is, the equitable outcome, is given by the egalitarian outcome.
So far we have stressed the importance of the concern for relative payoffs. This does not mean, however, that the absolute payoff should be viewed as a quantité negliable. Moreover, we do not claim that all people share a (similar) concern for an equitable share. In fact, many experiments have demonstrated the heterogeneity of subjects and the importance of absolute payoffs. A discussion on the heterogeneity of individual preferences is given, for example, in Parks (1994), Van Lange et al. (1997), and Kopelman et al. (this volume:Chapter 4). In this literature different types are discussed, such as cooperators, individualists, and competitors. In a similar vein, we assume that there are selfish people who care only for their material payoff and fair-minded people who reward fair and punish unfair behavior. As we will see, the interaction between these two types explains much of the observed data.
To be precise, in the Fehr and Schmidt model it is assumed that in addition to purely selfish subjects, there are subjects who dislike inequitable outcomes. They experience inequity if they are worse off in material terms than the other players in the experiment and they also feel inequity if they are better off. Moreover, it is assumed that, in general, subjects suffer more from inequity that is to their material disadvantage than from inequity that is to their material advantage. Formally,

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consider a set of n players indexed by i {1,…, n} and let π = (π1,…,πn) denote the vector of monetary payoffs. The utility function of player i is given by
(5-1)
where αi ≥ βi ≥ 0 and βi < 1.
The first term in Equation 5-1, πi, is the material payoff of player i. The second term in Equation 5-1 measures the utility loss from disadvantageous inequality, and the third term measures the loss from advantageous inequality. Figure 5-1 illustrates the utility of player i as a function of xj for a given income xi. Given his own monetary payoff xi, player i’s utility function obtains a maximum at xj = xi. The utility loss from disadvantageous inequality (xj > xi) is larger than the utility loss if player i is better off than player j (xj < xi).
To evaluate the implications of this utility function, let us start with the two player case. For simplicity the model assumes that the utility function is linear in inequality aversion as well as in xi. Furthermore, the assumption αi ≥ βi captures the idea that a player suffers more from inequality that is to his disadvantage. The paper mentioned by Loewenstein et al. (1989) provides strong evidence that this assumption is, in general, valid. Note that αi ≥ βi essentially means that a subject is loss averse in social comparisons: Negative deviations from the reference outcome count more than positive deviations. The model also assumes that 0 ≤
FIGURE 5-1 Preferences of inequity aversion.

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βi < 1. βi ≥ 0 means that the model rules out the existence of subjects who like to be better off than others. To interpret the restriction βi < 1, suppose that player i has a higher monetary payoff than player j. In this case βi = 0.5 implies that player i is just indifferent between keeping $1 to himself and giving this dollar to player j. If β = 1, then player i is prepared to throw away $1 in order to reduce his advantage relative to player j which seems very implausible. This is why we do not consider the case βi ≥ 1. On the other hand, there is no justification to put an upper bound on αi. To see this, suppose that player i has a lower monetary payoff than player j. In this case player i is prepared to give up $1 of his own monetary payoff if this reduces the payoff of his opponent by (1 + αi) / α i dollars. For example, if αi = 4, then player i is willing to give up $1 if this reduces the payoff of his opponent by $1.25.
If there are n > 2 players, player i compares his income to all other n – 1 players. In this case the disutility from inequality has been normalized by dividing the second and third term by n – 1. This normalization is necessary to make sure that the relative impact of inequality aversion on player i’s total payoff is independent of the number of players. Furthermore, we assume for simplicity that the disutility from inequality is self-centered in the sense that player i compares himself to each of the other players, but does not care per se about inequalities within the group of his opponents.
THEORETICAL PREDICTIONS
In the following text we discuss the impact of inequity aversion in typical common-pool resource games. The first game we analyze is a standard common-pool resource game without communication and sanctioning opportunities. We proceed by analyzing games that add the possibilities of costly sanctioning and communication, respectively. For all games we first derive the standard economic prediction, that is, the Nash equilibrium assuming that everybody is selfish and rational. We contrast this prediction with experimental results and the prediction derived by our fairness model. In presenting the experimental results, we restrict our attention to behavior of subjects in the final period because in that period, nonselfish behavior cannot be rationalized by the expectation of rewards in future periods. Furthermore, in the final period, we have more confidence that the players fully understand the game being played. The reason we do not analyze one-shot data (as, e.g., in Rutte and Wilke, 1985) is simple: To our knowledge there are no one-shot experiments where the same common-pool resource game has been studied in various environments. Only the repeated game data by Walker and colleagues (1990) allows this type of analysis because they studied the same game in various institutional setups. Of course the final period of a repeated interaction may be different in some way from a pure one-shot game. It has been argued, for example, that people might not sanction if they interact only once. This conjecture, however, clearly is refuted by recent experimental evidence

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showing that even in a pure one-shot game, many people engage in costly sanctions and punish defectors (Falk et al. 2000b).
The Standard Common-Pool Resource Game
In a standard common-pool resource game, each player is endowed with an endowment e. All n players in the group decide independently and simultaneously how much they want to appropriate from a common-pool resource. Individual i’s appropriation decision is denoted by xi. The appropriation decision causes a cost c per unit of appropriation but also yields a revenue. Although the cost is assumed to be independent of the decisions of the other group members, the revenue depends on the appropriation decisions of all players. More specifically, the total revenue of all players from the common-pool resource is given by ƒ(Σxj) where Σxj is the amount of total appropriation. For low levels of total appropriation ƒ(Σxj) is increasing in Σxj, but beyond a certain level ƒ(Σxj) is decreasing in Σxj. An individual subject i receives a fraction of ƒ(Σxj) according to the individual’s share in total appropriation Thus the total material payoff of i is given by:
In the experiments of Walker and colleagues (1990), e = 10 (or 25) and c = 5. The total revenue is given by ƒ(Σxj) = 23 Σxj – .25(Σxj)2. Thus in this experiment, material payoffs are:
Intuitively this is a social dilemma problem because individual i’s appropriation decision xi does not only affect player i’s payoff, but also that of all other players. Beyond a certain level of total appropriations, an increase in the appropriation of player i lowers the other players’ revenue from the common-pool resource. Because selfish players are concerned only with their own well-being, they do not care about the negative externalities they impose on others. As we will discuss, this leads to the typical inefficiencies that are characteristic for this type of dilemma games.
The above payoff function from Walker and colleagues can be transformed into πi = 10 + 18xi – 0.25xi Σxj or more abstractly as πi =: e + α xi – bxi Σxj. As we will see this notation will be useful in the following discussion.
In this common-pool resource game, the standard economic prediction (assuming completely selfish and rational subjects) is as stated in Proposition 1:4

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Proposition 1 (Selfish Nash Equilibrium)
If all players have purely selfish preferences, the unique Nash equilibrium is symmetric and individual appropriation levels are given by
In the following we denote this equilibrium as SNE (Selfish Nash Equilibrium) and the corresponding individual appropriation levels as xSNE. As can be seen from Proposition 1, the individual contribution is independent of the endowment and it is decreasing in the number of players. In the specification of Ostrom et al., groups of eight players participated in the experiment. Thus in their experiment the predicted individual contribution amounts to Given the group size, total appropriation is 64. Compared to the social optimum of 36, this equilibrium yields substantial inefficiencies.5 The point is that in their decisions, subjects ignore the negative externality imposed on the other players. Because players are assumed to care only about their own material payoff, they simply don’t care about such externalities.
How does the presence of inequity-averse or reciprocally motivated subjects alter the standard economic prediction? To answer this question, we will discuss two propositions. The first proposition considers symmetric equilibria whereas the second deals with asymmetric equilibria.
It is useful to start our discussion of the properties of symmetric equilibria with the nature of the best response function of an inequity-averse subject. The best response function indicates the optimal appropriation response of an inequity-averse player to the average appropriation of all other players. Figure 5-2 shows the best response of an inequity-averse subject (with positive α and β ) and compares it to that of a selfish subject. The thin line represents the optimal appropriation of a selfish subject given the average appropriation level of the other group members.6 As can be seen in Figure 5-2, a selfish player appropriates less, the more the other group members appropriate. At the point where the best response function intersects the diagonal, the SNE prevails. At this point the average appropriation level of the other n – 1 players is 8 from the viewpoint of each individual player. Moreover, it is in the self-interest of each player to respond to this average appropriation of the n – 1 other players with an own appropriation level of 8. Now look at the bold line in Figure 5-2. This line shows the best response behavior of an inequity averse subject. Four aspects of this function are important to emphasize.
First, in the area above the diagonal, that is, where the other players appropriate less than in the SNE, the best response curve of an inequity-averse player lies below that of a selfish player. This means that if the other players are “nice” in the sense that they appropriate less than what is in their material self-interest, an inequity-averse subject also appropriates less. Because inequity-averse players dislike being in a too favorable position, they do not exploit the kindness of the

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FIGURE 5-2 Best response behavior in a standard common-pool resource game (alpha = 4, beta = 0.6).
other players but instead voluntarily sacrifice some of their resources in favor of the other players.
Second, there is an area below the diagonal. In this area the other group members appropriate more than in the SNE. The best response behavior of an inequity-averse subject dictates to appropriate more than is compatible with pure self-interest in this case. Here, the intuition is that because the other players appropriate more than in the SNE, the inequity-averse player takes revenge by imposing negative externalities on the other players. The desire to take revenge results from the fact that the large appropriation levels of the others cause disadvantageous inequality for the inequity-averse subject. Because appropriating in this area reduces the payoff of the others more than their own payoff, an inequityaverse player can reduce the payoff differences. The selfish player, on the other hand, does not care about payoff differences and therefore appropriates less in this situation.
Third, a part of the inequity-averse player’s best response lies right on the diagonal. This is the area in which symmetric equilibria may exist. There may be equilibria in which subjects appropriate less than in the SNE as well as equilibria in which they appropriate more. Of particular interest are the equilibria to the left of the SNE because in this direction efficiency is increasing (up to the optimal appropriation level of 36). Whether such equilibria do exist depends on the distribution of the parameters α and β (see our discussion on Proposition 2).
Fourth, notice that in case the others do not appropriate at all the best re-

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sponses of selfish and inequity-averse players coincide. At first glance, this seems counterintuitive, because in a certain sense appropriating nothing is the most friendly choice of the other group members. However, the coincidence of the two best response functions at that point is quite sensible. The reason is that if the other group members do not appropriate at all, the appropriation decisions of a player do not affect the other players’ payoffs at all. This is because the other players’ share of the total revenue is zero. So why should an inequity averse-player not choose the money-maximizing appropriation level of 36 units? Remember that the utility function specified in equation 5-1 combines a concern for absolute income and for payoff differences. In case the other players do appropriate nothing, utility is equal to Ui = πi – βi (πi – π–i) = πi(1 – βi ) + βi π–i, where π–i is the individual payoff of each of the n – 1 other players who appropriate zero. Because π–i is equal to e, it does not depend on the choice of player i, and because βi < 1, it is clear that even for a highly inequity-averse subject, money-maximizing behavior and utility-maximizing behavior coincide.
Given the best response behavior of inequity-averse subjects, the existence conditions and the nature of symmetric equilibria are described in the next proposition. Note that in this proposition, min(βi ) denotes the smallest βi among all n players and min(α i) denotes the smallest α i.
Proposition 2 (Symmetric Equilibria with Inequity-Averse Subjects)
There is a symmetric equilibrium in which each subject chooses
The intuition of Proposition 2 is as follows: If both the smallest α i and the smallest βi are equal to zero, the only equilibrium is the SNE, that is, This means that the presence of only one egoistic player in the group (with α i = βi = 0) suffices to induce all other players to act in a selfish manner, regardless of how inequity averse they are. Put differently, a single egoist rules out any efficiency improvement compared to the SNE even if all other n – 1 players are highly inequity averse.
Proposition 2 entails a very strong result. It states that the subject with the “weakest preferences” for an equitable outcome dictates the outcome for the whole group. Only if the lowest α i or the lowest βi are greater than zero do asymmetric equilibria that differ from the SNE exist. Of particular interest are equilibria where the smallest βi is greater than zero. In this case the lower bound of the interval given in Proposition 2 is smaller than xSNE, that is, there are equilibria “to the left” of the SNE. In these equilibria subjects appropriate less than in the SNE. Similarly, if the smallest αi is larger than zero, there exist equilibria in

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Andreoni, J., and H. Varian 1999 Preplay contracting in the prisoner’s dilemma. Proceedings of the National Academy of Sciences 96:10933-10938.
Berg, J., J. Dickhaut, and K. McCabe 1995 Trust, reciprocity and social history. Games and Economic Behavior 10:122-142.
Bewley, T. 1998 Why not cut pay? European Economic Review 42:459-490.
Blau, P. 1964 Exchange and Power in Social Life. New York: Wiley.
Blount, S. 1995 When social outcomes aren’t fair: The effect of causal attributions on preferences. Organizational Behavior and Human Decision Processes 63(2):131-144.
Bohnet, I., and B.S. Frey 1999a The sound of silence in prisoner’s dilemma games. Journal of Economic Behavior and Organization 38:43-57.
1999b Social distance and other rewarding behavior in dictator games: Comment. American Economic Review 89:335-339.
Bolton, G.E., and A. Ockenfels 2000 A theory of equity, reciprocity and competition. American Economic Review 90:166-193.
Casari, M., and C. Plott 1999 Agents Monitoring Each Other in a Common-Pool Resource Environment. Working paper, California Institute of Technology, Pasadena.
Chamess, G., and M. Rabin 2000 Social Preferences: Some Simple Tests and a New Model. Working paper, University of California Berkeley.
Clark, A.E., and A.J. Oswald 1996 Satisfaction and comparison income. Journal of Public Economics 61:359-381.
Cooper, R., D. DeJong, R. Forsythe, and T. Ross 1992 Communication in coordination games. Quarterly Journal of Economics 107:739-771.
Davis, J.A. 1959 A formal interpretation of the theory of relative deprivation. Sociometry 102:280-296.
Dietz, T., and P.C. Stern 1995 Toward a theory of choice: Socially embedded preference construction. Journal of Socio-Economics 24(2):261-279.
Dufwenberg, M., and G. Kirchsteiger 1998 A Theory of Sequential Reciprocity. Discussion paper, Center for Economic Research, Tilburg University.
Falk, A., E. Fehr, and U. Fischbacher 2000a Testing Theories of Fairness: Intentions Matter. Working paper, Institute for Empirical Research, University of Zurich.
2000b Informal Sanctions. Working paper, Institute for Empirical Research, University of Zurich.
Falk, A., and U. Fischbacher 1998 A Theory of Reciprocity. Working paper 6, Institute for Empirical Research, University of Zurich.
Fehr, E., and S. Gächter 2000a Cooperation and punishment in public good experiments—An experimental analysis of norm formation and norm enforcement. American Economic Review 90:980-994.
2000b Fairness and retaliation: The economics of reciprocity. Journal of Economic Perspectives 14:159-181.
Fehr, E., G. Kirchsteiger, and A. Riedl 1993 Does fairness prevent market clearing? An experimental investigation. Quarterly Journal of Economics 108:437-460.

OCR for page 157

The Drama of the Commons
Falk, A., and M. Knell 2000 Choosing the Joneses: On the Endogeneity of Reference Groups? Working paper 53, Institute for Empirical Research, University of Zurich.
Fehr, E., and K. Schmidt 1999 A theory of fairness, competition, and cooperation. Quarterly Journal of Economics 114:817-851.
Festinger, L. 1954 A theory of social comparison processes. Human Relations 7:117-140.
Frey, B.S., and I. Bohnet 1995 Institutions affect fairness: Experimental investigations. Journal of Institutional and Theoretical Economics 151:286-303.
Gächter, S., and A. Falk 2000 Work motivation, institutions, and performance. In Advances in Experimental Business Research, R. Zwick and A. Rapoport, eds. Kluwer Academic Publishers. in press Reputation or Reciprocity—Consequences for the Labour Market. Submitted to Scandinavian Journal of Economics.
Gintis, H. 2000 Strong reciprocity and human sociality. Journal of Theoretical Biology.
Gordon, S. 1954 The economic theory of common-property resource: The fishery. Journal of Political Economy 62:124-142.
Güth, W., R. Schmittberger, and B. Schwarze 1982 An experimental analysis of ultimatum bargaining. Journal of Economic Behavior and Organization 3(3):367-388.
Hardin, G. 1968 The tragedy of the commons. Science 162:1243-1248.
Harsanyi, J., and R. Selten 1988 A General 7heory of Equilibrium Selection in Games. Cambridge, MA: MIT Press.
Homans, G.C. 1961 Social Behavior: Its Elementary Forms. New York: Harcourt, Brace & World.
Huck, S., and J. Oechssler 1996 The indirect evolutionary approach to explaining fair allocations. Games and Economic Behavior 28:13 -24.
Isaac, M.R., J.M. Walker, and A.M. Williams 1994 Group size and the voluntary provision of public goods. Journal of Public Economics 54:1-36.
Kerr, N., and C. Kaufmann-Gilliland 1994 Communication, commitment and coordination in social dilemmas. Journal of Personality and Social Psychology 66:513-529.
Kreps, D., P. Milgrom, J. oberts, and R. Wilson 1982 Rational cooperation in the finitely repeated Prisoners’ Dilemma. Journal of Economic Theory 27:245-252.
Ledyard, J. 1995 Public goods: A survey of experimental research. In Handbook of Experimental Economics, J. Kagel and A. Roth, eds. Princeton: Princeton University Press.
Levine, D. 1998 Modeling altruism and spitefulness in experiments. Review of Economic Dynamics 1:593-622.
Lind, E.A., and T.R. Tyler 1988 The Social Psychology of Procedural Justice. New York: Plenum Press.

OCR for page 157

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Loewenstein, G.F., L. Thompson, and M.H. Bazerman 1989 Social utility and decision making in interpersonal contexts. Journal of Personality and Social Psychology 57:426-44 1.
Moir, R. 1999 Spies and Swords: Behavior in Environments with Costly Monitoring and Sanctioning. Working paper, University of New Brunswick.
Ochs, J. 1995 Coordination problems. In Handbook of Experimental Economics, J. Kagel and A. Roth, eds. Princeton: Princeton University Press.
Ostrom E. 1990 Governing the Commons: The Evolution of Institutions for Collective Action. New York: Cambridge University Press.
1998 A behavioral approach to the rational choice theory of collective action—Presidential address of the American Political Science Association 1997. American Political Science Review 92:1-22.
Ostrom, E., R. Gardner, and J. Walker 1994 Rules, Games, and Common Pool Resources. Ann Arbor: University of Michigan Press.
Ostrom, E., and J. Walker 1991 Communication in a commons: Cooperation without external enforcement. Pp. 287-322 in Laboratory Research in Political Economy, T. Palfrey, ed. Ann Arbor: University of Michigan.
Ostrom, E., J. Walker, and R. Gardner 1992 Covenants with and without a sword: Self-governance is possible. American Political Science Review 40:309-317.
Palfrey, T., and J. Prisbrey 1997 Anomalous behavior in public goods experiments: How much and why? American Economic Review 87:829-846.
Parks, C.D. 1994 The predictive ability of social values in resource dilemmas and public goods games. Personality and Social Psychology Bulletin 20(4):431-438.
Pollis, N.P. 1968 Reference groups re-examined. British Journal of Sociology 19:300-307.
Rabin, M. 1993 Incorporating fairness into game theory and economics. American Economic Review 83(5):1281-1302.
Rocco, E., and M. Warglien 1995 Computer Mediated Communication and the Emergence of Electronic Opportunism. Working paper RCC 13659, Universita degli Studi di Venezia.
Runciman, W.G. 1966 Relative Deprivation and Social Justice. New York: Penguin.
Rutte, C.G., and H.A.M. Wilke 1985 Preference for decision structures in a social dilemma situation. European Journal of Social Psychology 15:367-370.
Sally, D. 1995 Conversation and Cooperation in Social Dilemmas: A Meta-Analysis of Experiments from 1958 to 1992. Rationality and Society 7(1):58-92.
Schwartz, S.H. 1977 Normative Influences on Altruism. Pp. 221-279 in Advances in Experimental Social Psychology Volume 10, L. Berkowitz, ed. New York: Academic Press.

OCR for page 157

The Drama of the Commons
1992 Universals in the content and structure of values: Theoretical advances and empirical tests in 20 countries. Pp. 1-65 in Advances in Experimental Social Psychology Volume 25, L. Berkowitz, ed. New York: Academic Press.
Selten, R. 1998 Features of experimentally observed bounded rationality. European Economic Review 42:413-436.
Sethi, R., and E. Somananthan 2000 Preference evolution and reciprocity. Journal of Economic Theory.
Stem, P.C., T. Dietz, G.A. Guagnano, and L. Kalof 1999 A Value-belief-norm theory of support for social movements: The case of environmentalism. Human Ecology Review 6(2):81-97
Van Lange, P.A.M., W. Otten, E.M.N. De Bruin, and J.A. Joireman 1997 Development of prosocial, individualistic, and competitive orientations: Theory and preliminary evidence. Journal of Personality and Social Psychology, 73:733-746.
de Waal, F. 1996 Good Natured. The Origins of Right and Wrong in Humans and Other Animals. Cambridge, MA: Harvard University Press.
Walker, J., R. Gardner, and E. Ostrom 1990 Rent dissipation in a limited access common-pool resource: experimental evidence. Journal of Environmental Economics and Management 19:203-211.
Yamagishi, T. 1986 The provision of a sanctioning system as a public good. Journal of Personality and Social Psychology 51:110-116.
APPENDIX TO CHAPTER 5
Proof Proposition 1 (Selfish Nash Equilibrium)
The standard common-pool resource game we look at has the following form:
Defining e=50, a=18 and b=0.25, we get:
πi = 50 + 18xi – 0.25xiΣxj
πi =:e + axi – bxi∑xj
To find the selfish best reply for xi,we calculate
Setting it equal to zero, we get as best reply
First suppose that all In this case

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Summing up the terms for all i, we get
Hence
Entering the sum into we get Now consider that there are some players who choose 0. Let n0 be the number of players who choose xi equal to zero. Then all values above zero must be equal to Calculating the best reply for one of the n0 players who originally played 0 now yields a contradiction. QED
Social optimum: To find the social optimum, we calculate
Hence, in the social optimum, we get
Proof of Proposition 2 (Symmetric Equilibria with Inequity-Averse Subjects)
First note that if the players who choose the higher appropriation level also have higher payoffs:
So let us first consider this case.
Suppose all players j ≠ i choose . Because Ui is concave in xi, the best reply is unique. So, to show that is the best reply, it is sufficient to show that it is a local optimum. It is clear that because otherwise player i could improve his material payoff as well as he could reduce inequity by increasing xi. It remains to check that there is no incentive for i to increase xi above . As the following calculation shows, the derivative from above is a linear function in x. So, player i has no incentive to increase above if this derivative equals at least zero.

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Thus, we get a critical condition for
(5-A)
The right-hand side of this inequality is decreasing in βi . Thus, the left inequality of the proposition is satisfied, if and only if (5-A) is satisfied for all i.
Assume now all other players j ≠ i choose Now, the critical condition is
Thus, we get a critical condition for
5-A(1)
The righthand side of this inequality is increasing in αi. Thus, the left inequality of the proposition is satisfied, if and only if 5-A(1) is satisfied for all i and we get the right inequality in the proposition.

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It remains to show that there is no equilibrium with appropriation decisions above We fix The critical condition is Because a decrease of the appropriation level now generates inequity in favor of player i, we get the following condition:
Because βi < 1, the last term is negative if xi is close to . Hence, there are no equilibria with
Proof of Proposition 3 (Asymmetric Equilibria with Inequity-Averse Subjects)
We first show (ii): Let us assume there is an equilibrium with some By reordering the players, we can assume that we have Furthermore, let k be the highest index for which Now let’s consider i ≤ k. Because we are in an equilibrium, we have Remember that πj – πi = (a – bΣxk) (xj - xi). So

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Hence
βi(k – 1) – αi(n – k) ≥ 0
or
which proves (ii).
Let us now come to the proof of (i). Assume without loss of generality that for i between 1 and k, we have This implies because We will show that there is an equilibrium with x1, = x2 =…= xk < xSNE. For x [0, xSNE] we define the strategy combination s(x) as follows: We fix s(x)i = x for i ≤ k and choose s(x)j for j > k as the joint best reply. That means that s(x)j is a part of a Nash equilibrium in the (n – k)-player game induced by the fixes choice of x by the first k players. Because at least half of the players choose x, the best reply can never be smaller than x (by increasing the appropriation level below x, the material payoff could be increased and the inequity disutility could be decreased as well). If we find , such that for i ≤ k, then is the desired equilibrium.

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Now
We then get
Hence, for some near enough to xSNE, we get The strategy combination s( ) is the desired equilibrium. QED
Proof of Proposition 4 (Equilibria with Sanctioning Possibilities)
Proof: We note:
(A) The condition guarantees that x maximizes the utility for the CCEs if all other players choose x.
We call a player a deviator who chooses an appropriation x’ that results in a higher payoff in the first stage compared to choosing x.
(B) If there is a single deviator, then the payoffs for the other players are smaller compared to the situation where there is no deviator.
First, if punishment is executed, the selfish players have no incentive to deviate. Because punishment results in equal payoffs for the CCEs and for the deviator, this payoff is smaller than the payoff in the first stage of the CCE. Hence, a selfish deviator has no incentive to deviate if he risks being punished.
Let us now prove that no CCE has an incentive to change the punishment strategy if a selfish player has not chosen x. Let πp be the payoff after punishment for the CCEs and for the deviator. Let πs be the payoff of the selfish players. A CCE player never has an incentive to choose a higher punishment than the equi

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librium punishment. This only increases inequity with respect to all players and reduces the material payoff. So let w be a positive number and assume CCE player i chooses a punishment of p – w instead of p. We get:
This is a linear function in w. Player i has no incentive to deviate iff the derivative with respect to w is negative, so iff
QED.

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