论文标题
在大型非convex聚合游戏中近似NASH平衡
Approximate Nash equilibria in large nonconvex aggregative games
论文作者
论文摘要
This paper shows the existence of $\mathcal{O}(\frac{1}{n^γ})$-Nash equilibria in $n$-player noncooperative sum-aggregative games in which the players' cost functions, depending only on their own action and the average of all players' actions, are lower semicontinuous in the former while $γ$-Hölder continuous in the latter.动作集和成本功能都不需要凸。对于一类重要的汇总游戏，其中包括$γ$等于1的拥塞游戏，使用梯度 - 高算法来构建$ \ Mathcal {o}（\ frac {1} {n} {n} {n} {n}）$ - NASH EQUILIBRIA，大多数$ \ Mathcal calcal calcal {o \ nathcal {o} n^n^3）$ ITARITACT。这些结果应用于有关电力系统需求侧管理的数值示例。说明了当$ n $倾向于无穷大时，该算法的渐近性能被说明。
This paper shows the existence of $\mathcal{O}(\frac{1}{n^γ})$-Nash equilibria in $n$-player noncooperative sum-aggregative games in which the players' cost functions, depending only on their own action and the average of all players' actions, are lower semicontinuous in the former while $γ$-Hölder continuous in the latter. Neither the action sets nor the cost functions need to be convex. For an important class of sum-aggregative games, which includes congestion games with $γ$ equal to 1, a gradient-proximal algorithm is used to construct $\mathcal{O}(\frac{1}{n})$-Nash equilibria with at most $\mathcal{O}(n^3)$ iterations. These results are applied to a numerical example concerning the demand-side management of an electricity system. The asymptotic performance of the algorithm when $n$ tends to infinity is illustrated.
