Correlated Play in Weakest-Link and Best-Shot Group Contests

Abstract

We explore public randomization (Harris et al., 1995) in group contests and introduce group public randomization equilibria (GPRE). We consider group all-pay auctions with weakest-link and best-shot impact functions. While best-shot contests without public randomization are known for their multiplicity of equilibria, introducing public randomization results in a unique GPRE in which only one of the strongest players in each group is active. However, in the weakest-link case, the well-known multiplicity of equilibria becomes even more pronounced with public randomization. GPRE without singleton support (non-degenerate) can be partially ordered according to first-order stochastic dominance. The dominant equilibrium yields the highest expected total effort among all equilibria, whether non-degenerate or not, yet it may not yield the lowest expected total payoff. Despite this multiplicity, a refinement that selects GPRE immune to coalitional deviations reduces the gamut of GPRE to a unique equilibrium group-effort distribution, which, for identical groups composed of identical agents, features the highest expected total effort among all equilibria of the full information game without correlation devices. The (weak) increase in expected efforts due to correlated strategies is also observed in the best-shot case.

Keywords: All-pay auction, correlated equilibrium, public randomization, best shot, weakest link.