Fairness and Desert in Tournaments

We develop a model to describe the behavior of agents who care about receiving their just deserts in competitive situations. In particular we analyze the strategic behaviour of two identical desert-motivated agents in a rank-order tournament. Each agent is assumed to be loss averse about an endogenous and meritocratically determined reference point that represents her perceived entitlement. Sufficiently strong desert concerns render the usual symmetric equilibrium unstable or non-existent and allow asymmetric desert equilibria to arise in which one agent works hard while the other slacks off. As a result, agents may prefer competition for status to a random allocation, even when the supply of status is fixed. When employees are desert-motivated we find that an employer may prefer a tournament to relative performance pay linear in the difference in the agents` outputs if output noise is sufficiently fat-tailed or if the employer can use the tournament to induce an asymmetric equilibrium.