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 equilibrium in which at least one agent might be bankrupted and a non borrowing equilibrium in which no agent is bankrupted. We prove that the former occurs when the agent taking loans is relatively poor and the future does not matter very much. This action represents the Despair Effect, in which severely handicapped agents take actions that jeopardize their existence in the long run but are currently helpful. We find conditions under which borrowing and non borrowing equilibria overlap and do not overlap. We provide an example in which no equilibrium exists.