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.

本文涉及具有无限期折扣贴现的非合作差异博弈。更确切地说，它是先前论文的续集[A. Fonseca-Morales和O. Hern'andez-Lerma，潜在差分游戏，Dynamic Games Appl。，8（2）（2018），第254-279页。]其中引入了连续时间潜在游戏的概念。也就是说，一个非合作的差分博弈，我们可以将其连续时间最优控制问题（OCP）与之关联，其解为原始博弈的Nash均衡。因此，发现或分析博弈的纳什均衡的性质将简化为OCP的最优解。在这里，我们研究差异游戏，即离散时间情况。首先，我们给出了几个温和的条件，对于这些条件，差异博弈是潜在差异博弈（PDG）。然后，我们通过几个示例和应用来说明我们的结果。