Production Shock Distribution and Risk Aversion in Multi-Agent-Tournaments

Abstract

We analyze how agents’ effort choice in multi-agent rank-order tournaments depend on the probability distribution of the random production shock and on the agents’ risk-aversion. If the shock is non-uniform, equilibrium effort depends on the number of winners and losers in the tournament. It is maximized when the share of winners corresponds to the relative location of the maximum density in the shock’s distribution. The effort choice of risk averse agents also depends on the number of winners and losers. It is possible that effort increases as agents become more risk-averse and that risk-averse agents exert more effort than risk-neutral agents when the tournament has more winners than losers. Unless agents are risk-neutral and liability is unlimited, the principal faces a complex trade-off between induced effort and total bonus payments. Her payoff may be higher with risk-averse agents than with risk-neutral agents if the number of winners is high.

Keywords: Incentives, Risk Aversion, Tournament, Contest, Order-Statistics, Principal-Agent Theory, Contracts

JEL Classification: D21, D23, J41, L14