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. (C) 2017, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.