Delegation in Strategic Environments and Equilibrium Uniqueness

TL;DR

This paper investigates conditions under which strategic games with delegation to intermediaries have unique equilibrium predictions, providing new insights into equilibrium robustness and applications in collusion-proof mechanism design.

Contribution

It characterizes when delegation outcomes via CCE or IRCP are unique, linking these concepts and offering new conditions for classical equilibrium uniqueness without relying on dominant strategies.

Findings

IRCP and CCE can be unique under certain game structures.

Classical equilibria are shown to be robust to various informational and perturbation factors.

Results have applications in designing collusion-proof mechanisms.

Abstract

We ask when a normal-form game yields a single equilibrium prediction, even if players can coordinate by delegating play to an intermediary such as a platform or a cartel. Delegation outcomes are modeled via coarse correlated equilibria (CCE) when the intermediary cannot punish deviators, and via the set of individually rational correlated profiles (IRCP) when it can. We characterize games in which the IRCP or the CCE is unique, uncovering a structural link between these solution concepts. Our analysis also provides new conditions for the uniqueness of classical correlated and Nash equilibria that do not rely on the existence of dominant strategies. The resulting equilibria are robust to players' information about the environment, payoff perturbations, pre-play communication, equilibrium selection, and learning dynamics. We apply these results to collusion-proof mechanism design.