Fooling Some of the People Some of the Time: Reputation Management and Optimal Betrayal

A rational long lived player plays against a series of short lived players who use a variant of the Adaptive Play behavioral rule. In equilibrium, under certain conditions, there will be a cut-off level of reputation. If their reputation is below the cut-off, they will build their reputation, and consume out of their reputation if it is above the cut-off. Over the long run, their reputation oscillates around the cut-off. A public relations professional can manipulate the sampling of the short lived players to the benefit of the long lived player. As a result a patient long lived player's behavior will worsen while an impatient long lived player's behavior will improve.