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Designing Cost-Sharing Methods for Bayesian Games.
Theory of Computing Systems ( IF 0.5 ) Pub Date : 2017-12-20 , DOI: 10.1007/s00224-017-9832-3
George Christodoulou 1 , Stefano Leonardi 2 , Alkmini Sgouritsa 1
Affiliation  

We study the design of cost-sharing protocols for two fundamental resource allocation problems, the Set Cover and the Steiner Tree Problem, under environments of incomplete information (Bayesian model). Our objective is to design protocols where the worst-case Bayesian Nash equilibria have low cost, i.e. the Bayesian Price of Anarchy (PoA) is minimized. Although budget balance is a very natural requirement, it puts considerable restrictions on the design space, resulting in high PoA. We propose an alternative, relaxed requirement called budget balance in the equilibrium (BBiE). We show an interesting connection between algorithms for Oblivious Stochastic optimization problems and cost-sharing design with low PoA. We exploit this connection for both problems and we enforce approximate solutions of the stochastic problem, as Bayesian Nash equilibria, with the same guarantees on the PoA. More interestingly, we show how to obtain the same bounds on the PoA, by using anonymous posted prices which are desirable because they are easy to implement and, as we show, induce dominant strategies for the players.

中文翻译:

设计贝叶斯游戏的费用分摊方法。

我们研究了信息不完全(贝叶斯模型)环境下两个基本资源分配问题(集合覆盖斯坦纳树问题)的成本共享协议的设计。我们的目标是设计协议,在这些协议中,最坏情况下的贝叶斯纳什均衡具有较低的成本,即将贝叶斯无政府状态价格(PoA)降至最低。尽管预算平衡是很自然的要求,但它对设计空间施加了很大的限制,从而导致较高的PoA。我们提出了另一种宽松的要求,称为平衡预算平衡(BBiE)。我们展示了遗忘随机算法之间的有趣联系低PoA的优化问题和成本分担设计。我们对这两个问题都利用这种联系,并且我们对随机问题采取了近似的解决方案,如贝叶斯纳什均衡,并在PoA上有同样的保证。更有趣的是,我们展示了如何通过使用匿名发布的价格来获得PoA上的相同界限,这是理想的,因为它们易于实现,并且如我们所示,可以为玩家提供主导策略
更新日期:2017-12-20
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