A game-theoretic analysis of bargaining with reputations

In this paper we introduce and discuss some models of bargaining. These have the form of repeated plays of a game among pairs of individuals, with the opponents in each particular game drawn randomly from a large population. The players' information about one another is limited to a single quantity, termed reputation, which summarizes the behavior of a player in previous trials of the game, and so changes endogenously. We distinguish some possible decision rules or “customs” which players might use to determine their moves in the game as a function of their own and their opponent's reputation, and investigate whether or not these actions lead to a suitably defined social equilibrium. We then compare the equilibrium customs from the point of view of the welfare of the population as a whole.