Correlated Equilibrium in Evolutionary Models with Subpopulations, Games and Economic Behavior
We study a version of the multipopulation replicator dynamics, where each population is comprised of multiple subpopulations. We establish that correlated equilibrium is a natural solution concept in this setting. Specifically, we show that every correlated equilibrium is equivalent to a stationary state in the replicator dynamics of some subpopulation model. We also show that every interior stationary state, Lyapunov stable state, or limit of an interior solution is equivalent to a correlated equilibrium. We provide an example with a Lyapunov stable limit state whose equivalent correlated equilibrium lies outside the convex hull of the set of Nash equilibria. Finally, we prove that if the matching distribution is a product measure, a state satisfying any of the three conditions listed above is equivalent to a Nash equilibrium.
Justin Lenzo, Todd Sarver
Lenzo, Justin, and Todd Sarver. 2006. Correlated Equilibrium in Evolutionary Models with Subpopulations. Games and Economic Behavior. 56(2): 271-284.