论文标题
在混合纳什平衡问题中寻求平衡的近端算法
Proximal-like algorithms for equilibrium seeking in mixed-integer Nash equilibrium problems
论文作者
论文摘要
我们考虑使用混合变量的潜在游戏，为此我们提出了两个分布式的，近端的平衡寻求算法。具体来说，我们专注于两种情况：i）基础游戏是广义的序数，并且代理通过选择确切的最佳策略来通过迭代来更新； ii）游戏承认了确切的潜力，并且代理商采用了近似的最佳响应。通过利用用作惩罚条款的整数兼容正规化函数的属性，我们表明算法都会收敛到精确或$ε$ - $ - $ - $ - $ - $ - $ - $ - 我们证实了我们的发现，以库诺特寡头模型的数值实例。
We consider potential games with mixed-integer variables, for which we propose two distributed, proximal-like equilibrium seeking algorithms. Specifically, we focus on two scenarios: i) the underlying game is generalized ordinal and the agents update through iterations by choosing an exact optimal strategy; ii) the game admits an exact potential and the agents adopt approximated optimal responses. By exploiting the properties of integer-compatible regularization functions used as penalty terms, we show that both algorithms converge to either an exact or an $ε$-approximate equilibrium. We corroborate our findings on a numerical instance of a Cournot oligopoly model.
