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首页> 外文期刊>ACM transactions on economics and computation >Existence and Efficiency of Equilibria for Cost-Sharing in GeneralizedWeighted Congestion Games
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Existence and Efficiency of Equilibria for Cost-Sharing in GeneralizedWeighted Congestion Games

机译：存在和效率的平衡费用分摊在GeneralizedWeighted拥堵游戏

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This work studies the impact of cost-sharing methods on the existence and efficiency of (pure) Nash equilibria in weighted congestion games.We also study generalized weighted congestion games, where each player may controlmultiple commodities.Our results are fairly general;we only require that our cost-sharing method and our set of cost functions satisfy certain natural conditions. For general weighted congestion games, we study the existence of pure Nash equilibria in the induced games, and we exhibit a separation from the standard single-commodity per player model by proving that the Shapley value is the only cost-sharing method that guarantees existence of pure Nash equilibria. With respect to efficiency, we present general tight bounds on the price of anarchy, which are robust and apply to general equilibrium concepts. Our analysis provides a tight bound on the price of anarchy, which depends only on the used cost-sharing method and the set of allowable cost functions. Interestingly, the same bound applies toweighted congestion games and generalized weighted congestion games. We then turn to the price of stability and prove an upper bound for the Shapley value cost-sharing method, which holds for general sets of cost functions and which is tight in special cases of interest, such as bounded degree polynomials. Also for bounded degree polynomials, we provide a somewhat surprising result, showing that a slight deviation from the Shapley value has a huge impact on the price of stability. In fact, for this case, the price of stability becomes as bad as the price of anarchy. Again, our bounds on the price of stability are independent on whether players are single or multi-commodity.
机译：这项工作研究费用分摊的影响方法的存在和效率(纯)纳什均衡在加权拥堵游戏。还研究广义加权拥堵游戏,每个玩家可能controlmultiple哪里大宗商品。只要求我们和我们的费用分摊方法组的成本函数满足某些自然条件。游戏,我们研究纯纳什的存在在诱导游戏平衡,我们表现出从标准矿产品/分离球员模型,证明夏普利值唯一的费用分摊方法保证纯纳什均衡的存在。效率,我们提出一般的严格界限的价格混乱,健壮和适用一般均衡概念。提供了一个严格约束无政府状态的价格,这只取决于使用费用分摊方法和容许成本函数的集合。有趣的是,相同的绑定应用toweighted交通拥堵游戏和广义加权交通拥堵的游戏。稳定和证明的一个上界沙普利值费用分摊方法,该基金持有对于一般的成本函数和集紧张感兴趣的在特殊情况下,如有界度多项式。度多项式,我们提供一个令人惊讶的结果,表明轻微从夏普利值有巨大的偏差影响价格的稳定。这种情况下,稳定的价格变得那么糟糕混乱的价格。价格是独立的是否稳定球员是单一或多种商品。

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