Population Games on 2-simplex: existence and efficiency of Nash equilibria

In this paper, we consider a two players dynamical game that evolves on a 2-simplex. By assuming that each player attempts to minimize a quadratic cost function, we show that there exists a unique Nash equilibria, which may be highly inefficient from the social optimum perspective. By taking advantage of this comprehensive characterization, we propose a technique to design perturbations in two populations dynamical games, with the aim of minimizing the price of anarchy under parameters constraints.