Almost pure nash equilibria in convex noncooperative games

Abstract

This paper considers n-person non-coalitional games with finite players' strategy spaces and payoff functions having some concavity or convexity properties. For such games it is shown that there are two-point Nash equilibria in them, that is equilibria in players' strategies with support consisting of at most two points. The structure of such simple equilibria is discussed in different cases. The results obtained in the paper can be seen as a discrete counterpart of Glicksberg's theorem and other known results about the existence of pure (or "almost pure") Nash equilibria in continuous concave (convex) games with compact convex spaces of players' pure strategies. © 2006 Springer-Verlag Berlin Heidelberg.