Hotelling-Downs Model with Limited Attraction
Hotelling-Downs Model with Limited Attraction
复制标题
吸引力有限的霍特林-唐斯模型
DOI：
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
Zihe Wang
中科院分区：
文献类型：
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作者：
Weiran Shen;Zihe Wang
在本文中，我们研究的变化标准的Hotelling-Downs模型的空间竞争，每个代理吸引客户端在一个有限的邻域，每个客户端随机选择一个有吸引力的代理服务。两个效用函数的代理被认为是：支持效用和赢家效用。我们将[Feldman et al. 2016]中的结果推广到客户端任意分布的情况。在支持效用设置，我们表明，一个纯粹的纳什均衡总是存在的制定游戏作为一个潜在的游戏。在赢家效用设置，我们表明，存在纳什均衡在两种情况下：当有最多3个代理，当吸引区域的大小至少是整个空间的一半。我们还考虑了无政府状态的代价和在一定条件下均衡的公平性。
In this paper we study variations of the standard Hotelling-Downs model of spatial competition, where each agent attracts the clients in a restricted neighborhood, and each client randomly picks one attractive agent for service. Two utility functions for agents are considered: support utility and winner utility. We generalize the results in [Feldman et al. 2016] to the case where the clients are distributed arbitrarily. In the support utility setting, we show that a pure Nash equilibrium always exists by formulating the game as a potential game. In the winner utility setting, we show that there exists a Nash equilibrium in two cases: when there are at most 3 agents and when the size of attraction area is at least half of the entire space. We also consider the price of anarchy and the fairness of equilibria under certain conditions.