Achieving symmetric Pareto Nash equilibria using biased replicator dynamics

Achieving the Nash equilibria for single objective games is known to be a computationally difficult problem. However there is a special class of equilibria called evolutionary robust equilibria which can be obtained through a special type of evolutionary dynamics called the replicator dynamics. This dynamics has special properties over the simplex, which has been studied in optimization theory to solve several combinatorial problems. In this work, we consider the essentially hard combinatorial optimization problem of computing the equilibria in games with multiple objectives. We extend the notion of replicator dynamics to handle such games. We establish proofs of dynamic stability of this modified replicator dynamics and present their relation to the Pareto Nash equilibria in multi-objective games.