Network Cost-Sharing without Anonymity

8 years 25 days ago

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We consider network cost-sharing games with non-anonymous cost functions, where the cost of each edge is a submodular function of its users, and this cost is shared using the Shapley value. Non-anonymous cost functions model asymmetries between the players, which can arise from diﬀerent bandwidth requirements, durations of use, services needed, and so on. These games can possess multiple Nash equilibria of wildly varying quality. The goal of this paper is to identify well-motivated equilibrium reﬁnements that admit good worst-case approximation bounds. Our primary results are tight bounds on the cost of strong Nash equilibria and potential function minimizers in network cost-sharing games with non-anonymous cost functions, parameterized by the set C of allowable submodular cost functions. These two worst-case bounds coincide for every set C, and equal the summability parameter introduced in [Roughgarden and Sundararajan, 2009] to characterize eﬃciency loss in a family of cost-sh...

Tim Roughgarden, Okke Schrijvers

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