Limited Records and Reputation

We study the impact of limited records on reputation dynamics, that is, how the set of equilibria and equilibrium payoffs changes in a model in which one long-lived player faces a sequence of short-lived players who observe only limited information about past play (the last K periods of the long-lived players actions). We show that limited records dramatically change the equilibrium behavior. Moreover, with limited records, equilibria in games with complete and incomplete information are strikingly different (in contrast to games with complete records). We also obtain a lower bound for equilibrium payoffs at any moment of the game, not only at the beginning, thus providing a stronger long-run prediction.