Reputation and Distribution in a Gift Giving Game

The folk theorem allows a very unequal division between players. In nonrepeated experimental games with many equilibria, such as ultimatum, observed play involves a relatively equal division between players. In a two-player repeated game setting there is a simple intuition about this: a poor player has little to lose by deviating from his equilibrium strategy. So a rich player ought to be willing to concede a reasonable amount of pie. We investigate whether reputation effects lead to this conclusion in a simple two person gift giving game. When types are known equilibria are socially feasible and pairwise individually rational. In the reputational case the set of equilibria is smaller than the set of socially feasible, average individually rational and incentive compatible payoffs, and larger than the set of socially feasible, pairwise individually rational and incentive compatible points. In general the set of equilibrium payoffs need not be smaller or more equitable in the reputational case. However, in sensible example, we can how the incentive constraints do have the desired effect of reducing the set of equilibrium payoffs and eliminating many inequitable equilibria. 1 The author is grateful for financial support from NSF grant SBR-9409180 and the UCLA Academic Senate. This paper benefited from conversations with Drew Fudenberg, David Kreps and Ed Prescott. 2 Department of Economics, UCLA, Los Angeles, CA 90024; e-mail: [email protected]