The Optimal Allocation of Prizes in Tournaments of Heterogeneous Agents

Abstract

Tournaments are widely used in organizations, explicitly or implicitly, to reward the best-performing employees, for example, by promotion or bonuses, and/or to penalize the worst-performing employees, for example, by demotion, withholding bonuses, or unfavorable job assignments. These incentive schemes can be interpreted as various prize allocations based on the employees' relative performance. While the optimal prize allocation in tournaments of symmetric agents is relatively well understood, little is known about the impact of the allocation of prizes on the effectiveness of tournament incentive schemes for heterogeneous agents. We show that while multiple prize allocation rules are equivalent when agents are symmetric in their ability, the equivalence is broken in the presence of heterogeneity. Under a wide range of conditions, loser-prize tournaments, that is, tournaments that award a low prize to relatively few bottom performers, are optimal for the firm. The reason is that low-ability agents are discouraged less in such tournaments, as compared to winner-prize tournaments awarding a high prize to few top performers, and hence can be compensated less to meet their participation constraints. (JEL M52, J33, J24)

Strive to be first or avoid being last: An experiment on relative performance incentives

“…Loser tournaments have more recently started to attract theoretical examinations by authors looking at heterogeneity in some aspect (e.g. Kräkel 2000, Gürtler and Kräkel 2011, Moldovanu, Sela and Shi 2012and Balafoutas et al 2012 or the effects of risk-aversion (Akerlof and Holden 2012).…”

Large Tournament Games

“…In economics, the analysis of tournaments goes back to the seminal paper of Lazear and Rosen (1981), which has inspired many papers that followed, including Akerlof and Holden (2012), Balafoutas et al (2017), Olszewski and Siegel (2017) and Fang et al (2018), among the more recent ones. Most of these works focus on finitely many players or static models.…”

Tournament rewards and heavy tails

“…The same will hold approximately for weakly asymmetric players as long as participation constraints are not binding (cf. Balafoutas et al, 2017). When players are strongly heterogeneous, the influence of noise is diminished and equilibrium characterization is difficult.…”

“…Starting with the groundbreaking paper by Lazear and Rosen (1981), multiple studies have explored optimal tournament contracts in an organizational context, comparing their efficiency to other incentive schemes, such as piece rates (Nalebuff and Stiglitz, 1983;Green and Stokey, 1983), and identifying their various properties pertaining to the number, risk-aversion and heterogeneity of agents (Krishna and Morgan, 1998;Akerlof and Holden, 2012;Balafoutas et al, 2017). 3 Yet, relatively little is known about the general properties of these incentive schemes pertaining to the shape of the distribution of noise.…”