Study on the interior equilibrium point of a special class of 2 × 2 × 2 asymmetric evolutionary games

Abstract

Many behavioural interactions in real life involve three individuals. When each individual has two alternative strategies, they can be abstracted into mathematical models by means of [Formula: see text] asymmetric games. In this paper, we explore a special class of [Formula: see text] asymmetric games satisfying fixed conditions. Firstly, we analyse two solitary interior equilibrium points and provide the judgement condition for their instability based on the Jacobi matrix local stability analysis method. Secondly, we analyse the interior equilibrium points that are continuously distributed within a line and probe into their stability conditions based on generalized Hamiltonian systems theory. Under the circumstances, the stable interior equilibrium point is surrounded by closed orbits in phase space, which presents an observable stable state where two strategies coexist and fluctuate in each of the three game populations. This work enriches the study of [Formula: see text] asymmetric games’ evolutionary dynamics.

Keywords

• evolutionary games
• 2 × 2 × 2 asymmetric games
• interior equilibrium point
• stability
• generalized Hamiltonian system