Utilitarian resource assignment
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- 作者：Petra Berenbrink ; Leslie Ann Goldberg ; Paul W. Goldberg ; Russell Martin
- 关键词：Congestion game ; Coordination ratio ; Nash Equilibrium
- 刊名：Journal of Discrete Algorithms
- 出版年：2006
- 出版时间：December 2006
- 年：2006
- 卷：4
- 期：4
- 页码：567-587
- 全文大小：227 K
文摘
This paper studies a resource allocation problem introduced by Koutsoupias and Papadimitriou. The scenario is modelled as a multiple-player game in which each player selects one of a finite number of known resources. The cost to the player is the total weight of all players who choose that resource, multiplied by the “delay” of that resource. Recent papers have studied the Nash equilibria and social optima of this game in terms of the l1"">l1&_user=3986987&_cdi=12928&_rdoc=7&_acct=C000050221&_version=1&_userid=10&md5=12e95285c0f7bc9dba88a381a5a3b992"" title=""Click to view the MathML source"">L∞ cost metric, in which the social cost is taken to be the maximum cost to any player. We study the L1 variant of this game, in which the social cost is taken to be the sum of the costs to the individual players, rather than the maximum of these costs. We give bounds on the size of the coordination ratio, which is the ratio between the social cost incurred by selfish behavior and the optimal social cost; we also study the algorithmic problem of finding optimal (lowest-cost) assignments and Nash Equilibria. Additionally, we obtain bounds on the ratio between alternative Nash equilibria for some special cases of the problem.