Competition and Equilibrium Effort Choice

Abstract

We examine optimal effort choice in a competition model where the agents are averse to low relative status and to exerting excessive effort. The game has a unique pure strategy Nash equilibrium. When the agents are homogeneous, a stronger competition incentive induces higher effort levels and results in lower utilities. When agents are heterogeneous, the model predicts that (i) all else equal, initial losers exert more effort but cannot become final winners, (ii) changes in effort choices of a subgroup of agents have a spillover effect, and (iii) agents with competitive advantages may prefer not to compete if the advantages are not significant enough. Some extensions and variants of the baseline model are also examined. Overall, the model's theoretical predictions are consistent with some competition-related findings documented in the empirical literature.

Keywords: costly effort, competition, relative status concern, Nash equilibrium

JEL Classification: C70, C72