Potential difference games and applications

This paper concerns noncooperative difference games with infinite horizon discounted payoffs. More precisely, it is a sequel to a previous paper [A. Fonseca-Morales and O. Hern'andez-Lerma, Potential differential games, Dynamic Games Appl., 8(2) (2018), pp. 254-279.] where the notion of continuous-time potential games was introduced. That is, a noncooperative differential game to which we can associate a continuous-time optimal control problem (OCP) whose solutions are Nash equilibria for the original game. Thus, finding or analysing the properties of Nash equilibria for the game reduces to that of the optimal solution of an OCP. Here, we study difference games, that is, the discrete-time case. First, we give several mild conditions for which a difference game is a potential difference game (PDG). Then, we illustrate our results with several examples and applications.