Abstract
We examine equilibrium selection in a two-stage sequential elimination contest in which contestants compete for a single prize. This game has a continuum of equilibria, only one of which satisfies the Coalition-Proof Nash Equilibrium (CPNE) refinement. That equilibrium involves burning out by using all of one's resources in the first stage. It is Pareto-dominated by many other equilibria. We find that CPNE predicts well when four people compete, but not when eight people compete for two second-stage spots. Using a cognitive hierarchy (CH) framework, we show that when the number of players and the mean number of thinking steps are large, the CH prediction involves burning out. This provides a partial explanation of our results. We also develop a formal argument as to why CPNE logic is more compelling with more players. We conclude that more competition leads to higher bids, and that burning out is indeed a competitive phenomenon.
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