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摘要翻译：
利用非光滑最佳响应函数导出了一类二次多领导-跟随对策的Nash平衡点。为了克服非光滑性的挑战，我们寻求一种光滑化方法，从而将其重新表述为光滑的纳什均衡问题。证明了所有光滑参数解的存在唯一性。对于这些平滑参数的递减序列存在Nash均衡的积累点，我们证明了这些候选点满足S-平稳性条件，并且是多领导-跟随博弈的Nash均衡。最后，为了提高计算效率，我们对引导变量进行了改进，并对非光滑牛顿法和次梯度法进行了数值比较。
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英文标题：
《Solving Quadratic Multi-Leader-Follower Games by Smoothing the
Follower's Best Response》
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作者：
Michael Herty, Sonja Steffensen, Anna Th\"unen
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最新提交年份：
2020
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分类信息：
一级分类：Mathematics 数学
二级分类：Optimization and Control 优化与控制
分类描述：Operations research, linear programming, control theory, systems theory, optimal control, game theory
运筹学，线性规划，控制论，系统论，最优控制，博弈论
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一级分类：Economics 经济学
二级分类：Theoretical Economics 理论经济学
分类描述：Includes theoretical contributions to Contract Theory, Decision Theory, Game Theory, General Equilibrium, Growth, Learning and Evolution, Macroeconomics, Market and Mechanism Design, and Social Choice.
包括对契约理论、决策理论、博弈论、一般均衡、增长、学习与进化、宏观经济学、市场与机制设计、社会选择的理论贡献。
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英文摘要：
We derive Nash equilibria for a class of quadratic multi-leader-follower games using the nonsmooth best response function. To overcome the challenge of nonsmoothness, we pursue a smoothing approach resulting in a reformulation as a smooth Nash equilibrium problem. The existence and uniqueness of solutions are proven for all smoothing parameters. Accumulation points of Nash equilibria exist for a decreasing sequence of these smoothing parameters and we show that these candidates fulfill the conditions of s-stationarity and are Nash equilibria to the multi-leader-follower game. Finally, we propose an update on the leader variables for efficient computation and numerically compare nonsmooth Newton and subgradient methods.
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PDF链接：
https://arxiv.org/pdf/1808.07941
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