Gambling in Dynamic Contests

This paper presents a strategic model of risk-taking behavior in the framework of a continuous time contest. Formally, we analyze a dynamic game in which each player decides when to stop a privately observed Brownian Motion with drift. Only the player who stops his process at the highest value wins a prize. We derive a closed-form solution for the unique Nash equilibrium outcome in mixed strategies and we establish that the expected value of the stopped stochastic processes is non-monotone in the drift. In particular, the highest losses in terms of expected value occur if the drift is only moderately negative. Thus, relative performance payments, while suitable to provide the right incentives in good times, induce socially undesirable gambling activities if times are moderately bad. Possible applications of the model include contests for status, job promotion contests, competition between mutual funds, and relative payment schemes of CEOs