While players may be almost certain of the payoffs and the structure of the game, they cannot be absolutely certain. This small room for doubt, when exploited by a very patient (dominant) player, leads to reputation being built. Here is what we know from the previous literature. A sufficiently patient dominant player facing a single opponent can exploit the incomplete information and guarantee payoffs that are arbitrarily close to the dynamic Stackelberg payoff, which is the best he can obtain subject to giving the other player at least the minmax payoff. My results stand in sharp contrast to the extant literature: introducing competition in the form of multiple long-lived opponents can severely restrict the dominant player’s ability to build and exploit reputation, in some cases completely nullifying it. It is consistent with some empirical observations that market sharing is uneven when there are two firms in the market, but more equitable when there are three or more firms.

scoco@ceibs.edu