论文标题
带有不平等约束的开环电位差异游戏
Open-loop potential difference games with inequality constraints
论文作者
论文摘要
静态潜在游戏是非合作游戏，它接受虚拟功能，也称为潜在功能，因此该功能的最小化器构成了相关非合件游戏的NASH平衡策略的子集（或改进）。在本文中，我们研究了$ n $ n $ - 玩家非零的差异游戏，并具有不平等约束，这些差异承认潜在的游戏结构。特别是，我们为存在最佳控制问题（具有不平等约束）的存在提供条件，以使该问题的解决方案产生相应的动态非合件游戏的开环NASH平衡策略（具有不平等约束）。此外，我们提供了一种构建与此最佳控制问题相关的潜在功能的方法。我们将一般结果专注于线性季节环境，并提供了基于线性互补性问题的方法来计算开环NASH均衡的改进。我们以一个受智能网格中的储能激励措施启发的示例来说明结果。
Static potential games are non-cooperative games which admit a fictitious function, also referred to as a potential function, such that the minimizers of this function constitute a subset (or a refinement) of the Nash equilibrium strategies of the associated non-cooperative game. In this paper, we study a class $N$-player non-zero sum difference games with inequality constraints which admit a potential game structure. In particular, we provide conditions for the existence of an optimal control problem (with inequality constraints) such that the solution of this problem yields an open-loop Nash equilibrium strategy of the corresponding dynamic non-cooperative game (with inequality constraints). Further, we provide a way to construct potential functions associated with this optimal control problem. We specialize our general results to a linear-quadratic setting and provide a linear complementarity problem-based approach for computing the refinements of the open-loop Nash equilibria. We illustrate our results with an example inspired by energy storage incentives in a smart grid.
