David K. Levine

March 18, 1995

Revised: December 7, 1996

* Abstract:* The folk theorem allows a very unequal division
between players. In non-repeated 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.