-Hardness of Pure Nash Equilibrium in Scheduling and Connection Games

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-Hardness of Pure Nash Equilibrium in Scheduling and Connection Games
We prove NP-hardness of pure Nash equilibrium for some problems of scheduling games and connection games. The technique is standard: first, we construct a gadget without the desired property and then embed it to a larger game which encodes a NP-hard problem in order to prove the complexity of the desired property in a game. This technique is very efficient in proving NP-hardness for deciding the existence of Nash equilibria. In the paper, we illustrate the efficiency of the technique in proving the NP-hardness of deciding the existence of pure Nash equilibria of Matrix Scheduling Games and Weighted Connection Games. Moreover, using the technique, we can settle the complexity not only of the existence of equilibrium but also of the existence of good cost-sharing protocol. Key words: Nash equilibrium, NP-hardness.
Nguyen Kim Thang
Added 17 Mar 2010
Updated 17 Mar 2010
Type Conference
Year 2009
Authors Nguyen Kim Thang
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