Nash equilibrium and group strategy consensus of networked evolutionary game with coupled social groups

Abstract

This paper studies the existence of Nash equilibrium and group strategy consensus problem of networked evolutionary game with coupled social groups, which is formulated as a two-layer networked game. First, by the approach of semi-tensor product, the payoff functions of players are converted into the algebraic forms, and two necessary and sufficient conditions are derived for the existence of pure Nash equilibrium. Second, the strict game algebraic equation by the best response adjustment rule with group intelligence is established, by which the group strategy consensus problem is investigated. At last, an example is worked out to verify our conclusions.