Generalized Means and Randomization Scheme of Nash Equilibria

Abstract

In this paper, a class of generalized convex games is introduced. Existence properties of Nash equilibria, in mixed and pure strategies, are proposed. These properties are studied by considering limit cases related to a specific class of semi-lattice games. We propose an interpretation of our results based on Atkinson’s notion of generalized means. We also show that our approach makes it possible to propose a preference scheme taking into account the notion of prioritarianism.