Dynamic Contests with Bankruptcy: The Despair Effect

Abstract

We analyze a two period contest in which agents may become bankrupt at the end of the …first period. A bankrupt agent is excluded from the contest in the second period of the game. We investigate the existence of a subgame perfect equilibrium in pure strategies. We distinguish between a borrowing equilibrum where at least an agent might be bankrupt and a non borrowing equilibrium where no agent is bankrupted. We prove that the former occurs when the agent taking loans is relatively poor. This is the despair effect where severely handicapped agents take actions that are risky. We also show conditions under which both kind of equilibria overlap or not. We provide an example in which no equilibrium exists.