Repeated contests with commitment types

Abstract

Contestants fight in repeated contests and privately know whether they are rational utility maximizers or automatons committed to always fighting “all-in.” In the unique symmetric equilibrium, rational contestants fight all-in in early contests as doing so buys a beneficial “all-in look” that intimidates rivals in future contests. In equilibrium, several structural differences emerge between periods in which multiple contestants maintain an all-in look, as opposed to one: most prominently, only in the former case aggregate efforts may exceed the per-period prize, and only in the latter payoffs can be positive.