Correlated optimin
For game theorists, this provides a new solution concept that improves upon correlated equilibrium by offering higher guaranteed payoffs in some games.
This paper extends the optimin concept from mixed strategies to correlated distributions, defining correlated optimins as Pareto optimal with respect to guaranteed payoffs under recommendation-contingent deviations. It proves existence in all finite games and shows that correlated optimins can strictly Pareto dominate correlated equilibria, as demonstrated in a 2x2 game.
We extend the optimin notion of Ismail (2025) from mixed strategy profiles to correlated distributions. A correlated distribution is evaluated by the worst expected payoff each player can receive when opponents may either obey their private recommendations or make unilateral recommendation-contingent deviations that are strictly profitable under the posterior induced by the distribution. Correlated optimins are Pareto optimal with respect to this vector of guaranteed payoffs. We show that a correlated optimin exists in every finite game. In addition, for every correlated equilibrium, there exists a correlated optimin such that every player's guaranteed payoff is weakly higher than his or her correlated equilibrium payoff. In two-player zero-sum games, correlated optimin coincides with correlated equilibrium and yields the maximin value. Outside zero-sum games, correlated optimin may strictly improve upon all correlated equilibria. We illustrate this with a simple 2x2 game with a unique correlated and coarse correlated equilibrium, in which there exists a correlated optimin that strictly Pareto dominates the equilibrium payoff.