A class of game models with equilibrium, stable and pareto-optimal solutions

Abstract

The paper proposes game models with pay-off functions being convolutions by the operation of taking minimum of two criteria one of which describes competition of players in some common (external) sphere of activity and the other describes private achievements of each player (in internal sphere). Strategies of players are distributions of resources between external and internal spheres. The first criterion of each player depends on strategies of all players; the second depends only on the strategy of given player. It is shown that, under some natural assumptions of the monotonicity of the criteria, such $n$-person games are characterized by the fact that the Nash equilibrium exists, is strong, stable, and Pareto-optimal, and in two-person games in the Stackelberg equilibrium, the leader and the follower win no less than in the Nash equilibrium.