Dynamical analysis of a game network

In this paper, our purpose is to establish a direct dynamical relationship between payoffs of players in a game. A network dynamical model is first proposed to describe the direct dynamical relationship. A Markovian chain is also introduced in the given network model to show the mixed strategy property in a game. As a result, a direct dynamical relationship between payoffs of players in a game can be illustrated through a network model with a Markovian chain. In addition, a sufficient condition is addressed to guarantee that the discussed network model has a unique and stable Nash equilibrium. Finally, a numerical example is shown to illustrate the effectiveness of the obtained criterion.