Aggregative games have many industrial applications, and computing an equilibrium in those games is challenging when the number of players is large. In the framework of atomic aggregative games with coupling constraints, we show that variational Nash equilibria of a large aggregative game can be approximated by a Wardrop equilibrium of an auxiliary population game of smaller dimension. Each population of this auxiliary game corresponds to a group of atomic players of the initial large game. This approach enables an efficient computation of an approximated equilibrium, as the variational inequality characterizing the Wardrop equilibrium is of smaller dimension than the initial one. This is illustrated on an example in the smart grid context.

中文翻译：

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具有耦合约束的大型聚合博弈中均衡的有效估计

聚合博弈有很多工业应用，当玩家数量很大时，计算这些博弈中的均衡是具有挑战性的。在具有耦合约束的原子聚合博弈的框架中，我们表明大型聚合博弈的变分纳什均衡可以通过较小维度的辅助种群博弈的 Wardrop 均衡来近似。这个辅助博弈的每个种群对应于初始大博弈的一组原子玩家。这种方法可以有效计算近似均衡，因为表征 Wardrop 均衡的变分不等式的维度比初始均衡小。这在智能电网上下文中的示例中进行了说明。