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.
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