Continuity and sensitivity analysis of parameterized Nash games
Continuity and sensitivity analysis of parameterized Nash games
复制标题
参数化纳什博弈的连续性和敏感性分析
DOI：
10.1007/s40505-022-00228-0
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发表时间：
2020
影响因子：
0.3
通讯作者：
Zachary Feinstein
中科院分区：
文献类型：
--
作者：
Zachary Feinstein
在本文中，我们考虑纳什均衡集的连续性以及参数化博弈的近似纳什均衡。对于具有独特纳什均衡的参数化博弈，这种均衡映射的连续性是众所周知的。然而，当平衡不需要唯一时，平衡映射中可能存在不连续性。由于游戏的参数需要在实践中进行估计，因此这些不连续性可能会导致对纳什均衡的错误理解，从而导致玩家的决策不正确。这项工作的重点是总结参数化纳什均衡的连续性属性，并通过在潜在非紧策略空间上具有一致连续目标函数的近似纳什博弈来证明连续性。也就是说，我们考虑纳什均衡集的鲁棒表示，以便参数的小扰动会导致纳什均衡集的微小变化。
In this paper we consider continuity of the set of Nash equilibria and approximate Nash equilibria for parameterized games. For parameterized games with unique Nash equilibria, the continuity of this equilibrium mapping is well-known. However, when the equilibria need not be unique, there may exist discontinuities in the equilibrium mapping. Because the parameters of a game need to be estimated in practice, these discontinuities can result in an incorrect understanding of the Nash equilibria and, thus also, the decision-making of the players. The focus of this work is to summarize continuity properties for parameterized Nash equilibria and prove continuity via the approximate Nash game with uniformly continuous objective functions over potentially non-compact strategy spaces. That is, we consider a robust representation for the set of Nash equilibria so that small perturbations in the parameters lead to small changes in the set of Nash equilibria.