The Drama of the Commons (2002) / Chapter Skim
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5 Appropriating the Commons: A Theoretical Explanation
5 Appropriating the Commons: A Theoretical Explanation
Pages 157-192
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From page 157... ...
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 appro157
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From page 158... ...
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.
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From page 159... ...
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.
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From page 160... ...
, 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.
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From page 161... ...
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.
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From page 162... ...
Given his own monetary payoff xi, player i's utility function obtains a maximum at x; = xi. The utility loss from disadvantageous inequality (x; > xi)
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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.
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From page 164... ...
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.
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From page 165... ...
= 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.
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From page 166... ...
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.
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From page 167... ...
Only if the lowest oci or the lowest ,Bi are greater than zero do asymmetric equilibria that differ from the SNE exist. Of particular interest are equilibria where the smallest ,Bi is greater than zero.
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From page 168... ...
In this equilibrium at least k players choose the same appropriation x < XSNE; the other players j choose higher appropriation levels. (iiJ If there is no k such that there are at least k players with Hi > _ then there is no equilibrium with less appropriation than in the SNE.
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From page 169... ...
(1994) report that average final period appropriation levels in three different groups were 63, 64, and 78 (in case the endowment was 25 tokens)
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From page 170... ...
, the prospects for more efficient appropriation levels are clearly improved in a common-pool resource environment with sanctioning possibilities. Precise conditions for the existence of equilibria with appropriation levels below the SNE are given in the following proposition.
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From page 171... ...
The conditions that oci and ,Bi have to meet are tougher when sanctioning is ruled out. Put differently, for a given distribution of inequityaverse and selfish players, it may be impossible to reach an equilibrium with a cooperative outcome when sanctioning is impossible, while there are equilibria with a cooperative outcome when sanctioning is possible.
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From page 172... ...
Although reciprocity-based punishments (as observed in the experiment already discussed) and repeated game incentives seem to be compatible with a cooperative atmosphere (Gachter and Falk, 2000)
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From page 173... ...
In terms of material payoffs, the game could look like the one expressed in Table 5-la, that is, the common-pool resource game is similar to a prisoners' dilemma game. Even though it is in their common interest to choose the low appropriation level, both players can individually improve their material payoffs if they choose the high appropriation strategy.
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From page 174... ...
If, for example, player 1 chooses the low appropriation strategy, player 2 with reciprocal preferences is better off choosing the low instead of the high appropriation level and vice versa. Even though players forgo some material payoffs, they have a higher utility if they reciprocate the nice behavior of the other player.
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From page 175... ...
Taken together, we have described two potential channels through which communication may elicit cooperative behavior in the presence of reciprocal preferences. Although the first rests only on the exchange of information, the second is built on the possibility of communication face to face.
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From page 176... ...
In fact, public goods games and common-pool resource games are very similar. Whereas in a common-pool resource game, subjects' decisions impose negative externalities on other subjects, subjects in a public goods game produce positive externalities.
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report that in the final period of public goods games without punishment, the vast majority of subjects play the equilibrium strategy of complete free riding. On average, 73 percent of all subjects choose gi = 0 in the final period.
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From page 178... ...
As long as only a few players are willing to contribute if others contribute as well, they would suffer too much from the disadvantageous inequality caused by the free riders. Thus, inequity-averse players prefer to defect if they know there are selfish players.
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If, on the other hand, subjects dispose of sanctioning possibilities, the reciprocal subjects are able to discipline selfish players. As a consequence, more cooperative outcomes will emerge.
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From page 180... ...
In such repeated interaction, players usually can condition their behavior on past behavior of others. This allows players to build up reputations and to ensure cooperative outcomes, even among selfish players.
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9 We concentrate on the behavior of subjects in the final periods to exclude the possible confound of repeated games effects and to make behvior comparable to our one-shot predictions. 10 A sanctioning institution was first studied by Yamagishi (1986)
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American Economic Review 90:980-994. 2000b Fairness and retaliation: The economics of reciprocity.
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Lind, E.A., and T.R. Tyler 1988 The Social Psychology of Procedural Justice.
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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.
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From page 185... ...
Journal of Personality and Social Psychology 51: 110- 116. APPENDIX TO CHAPTER 5 Proof Proposition 1 (Selfish Nash EquilibriumJ The standard common-pool resource game we look at has the following form: Hi = 50 - 5xi + [I;' ~~23>,xj -.25(>,xj)
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From page 186... ...
So, to show that xi = x is the best reply, it is sufficient to show that it is a local optimum. It is clear that xi 2 x because otherwise player i could improve his material payoff as well as he could reduce inequity by increasing xi.
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From page 187... ...
(1 Pi ) ~ibxi Thus, we get a critical condition for X7*
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From page 188... ...
2 O Because a nb nb dxi decrease of the appropriation level now generates inequity in favor of player i, we get the following condition: O< DU.
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From page 189... ...
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)
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From page 190... ...
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.
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From page 191... ...
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