PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Strong Equilibrium in Cost-Sharing Connection Game
Amir Epstein, Michal Feldman and Yishay Mansour
In: The Eighth ACM Conference on Electronic Commerce 2007, June 8-16, 2007, San Diego, CA, USA.

Abstract

In this work we study cost sharing connection games, where each player has a source and sink he would like to connect, and the cost of the edges is either shared equally (fair con- nection games) or in an arbitrary way (general connection games). We study the graph topologies that guarantee the existence of a strong equilibrium (where no coalition can improve the cost of each of its members) regardless of the speci¯c costs on the edges. Our main existence results are the following: (1) For a single source and sink we show that there is always a strong equilibrium (both for fair and general connection games). (2) For a single source multiple sinks we show that for a series parallel graph a strong equilibrium always exists (both for fair and general connection games). (3) For multi source and sink we show that an extension parallel graph always admits a strong equilibrium in fair connection games. As for the quality of the strong equilibrium we show that in any fair connection games the cost of a strong equilibrium is £(log n) from the optimal solution, where n is the number of players. (This should be contrasted with the ­(n) price of anarchy for the same setting.) For single source general connection games and single source single sink fair connec- tion games, we show that a strong equilibrium is always an optimal solution.

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EPrint Type:Conference or Workshop Item (Paper)
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Theory & Algorithms
ID Code:3000
Deposited By:Yishay Mansour
Deposited On:20 May 2007