Delegation in Strategic Environments and Equilibrium Uniqueness

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.

Figures (2)

• Figure 1: Expected payoff matrix for $m=3$ locations. Entries are $(u_1,u_2)$.
• Figure 2: Success functions in ratio-based contests for which the symmetric pure Nash equilibrium is the unique pure CCE and the equilibrium effort equals $1/4$. The dashed curve is the Tullock contest. The red curve, $\underline{p}_1$, is the most meritocratic contest. The blue curve, $\overline{p}_1$, is the least discriminatory: each contestant receives a participation bonus of at least $1/4$ of the prize.

Theorems & Definitions (32)

• Proposition 3.1
• proof
• Definition 3.1
• Lemma 3.1
• proof
• Theorem 3.1
• proof
• Proposition 3.2
• Lemma 4.1
• proof