We study public goods games, a type of game where every player has to decide whether or not to produce a good which is , i.e., neighboring players can also benefit from it. Specifically, we consider a setting where the good is indivisible and where the neighborhood structure is represented by a directed graph, with the players being the nodes. Papadimitriou and Peng (2023) recently showed that in this setting computing mixed Nash equilibria is -hard, and that this remains the case even for -well-supported approximate equilibria for some sufficiently small constant . In this work, we strengthen this inapproximability result by showing that the problem remains -hard for any non-trivial approximation parameter .

中文翻译：

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公共物品博弈中纳什均衡的紧不可逼近性

我们研究公共物品博弈，这是一种博弈类型，每个参与者都必须决定是否生产某种物品，即相邻参与者也可以从中受益。具体来说，我们考虑这样一种设置，其中商品是不可分割的，并且邻域结构由有向图表示，其中玩家是节点。Papadimitriou 和 Peng（2023）最近表明，在这种情况下计算混合纳什均衡是困难的，并且即使对于一些足够小的常数 的良好支持的近似均衡，情况仍然如此。在这项工作中，我们通过证明该问题对于任何非平凡的近似参数仍然是困难的来强化了这种不可近似性结果。