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Strategyproof mechanisms for 2 -facility location games with minimax envy
Journal of Combinatorial Optimization ( IF 1 ) Pub Date : 2021-02-23 , DOI: 10.1007/s10878-021-00711-7
Xin Chen , Qizhi Fang , Wenjing Liu , Yuan Ding , Qingqin Nong

We study a fairness-based model for 2-facility location games on the real line where the social objective is to minimize the maximum envy over all agents. All the agents seek to minimize their personal costs, and the envy between any two of them is the difference in their personal costs. We consider two cases of personal costs, called min-dist cost and sum-dist cost. We are interested in pursuing strategyproof mechanisms for 2-facility location games in both cases. For the min-dist personal cost, we first show that a lower bound of the additive approximation for any deterministic strategyproof mechanism is 1/4, then devise a deterministic group strategyproof mechanism with additive approximation of 1/2 and two randomized strategyproof mechanisms with additive approximation of 1/4. For the sum-dist personal cost, we devise a group strategyproof deterministic mechanism which is also optimal.



中文翻译:

带有minimax羡慕的2设施定位游戏的策略验证机制

我们在现实路线上研究了基于2个场所的定位游戏的基于公平的模型,其社会目标是最大程度地减少对所有特工的最大嫉妒。所有代理商都试图将他们的个人成本降到最低,而他们两个之间的嫉妒是他们的个人成本之差。我们考虑两种情况的个人成本,分别称为最小距离成本和总距离成本。在这两种情况下,我们都有兴趣为2设施定位游戏寻求策略验证机制。对于最小距离个人成本,我们首先证明任何确定性策略证明机制的加法近似下界为1/4,然后设计具有加法近似值1/2的确定性组策略证明机制和两个带加法的随机策略证明机制近似为1/4。对于总和个人成本,

更新日期:2021-02-23
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