Title: The impact of network topology on pure Nash equilibria in graphical games
Abstract:Graphical games capture some of the key aspects relevant to the study and design of multi-agent systems. It is often of interest to find the conditions under which a game is stable, i.e., the players ...Graphical games capture some of the key aspects relevant to the study and design of multi-agent systems. It is often of interest to find the conditions under which a game is stable, i.e., the players have reached a consensus on their actions. In this paper, we characterize how different topologies of the interaction network affect the probability of existence of a pure Nash equilibrium in a graphical game with random payoffs. We show that for tree topologies with unbounded diameter the probability of a pure Nash equilibrium vanishes as the number of players grows large. On the positive side, we define several families of graphs for which the probability of a pure Nash equilibrium is at least 1-1/e even as the number of players goes to infinity. We also empirically show that adding a small number of connection shortcuts can increase the probability of pure Nash.Read More
Publication Year: 2007
Publication Date: 2007-07-22
Language: en
Type: article
Access and Citation
Cited By Count: 12
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