Graphical Models for Game Theory
UAI '01 Proceedings of the 17th Conference in Uncertainty in Artificial Intelligence
Pure Nash equilibria: hard and easy games
Proceedings of the 9th conference on Theoretical aspects of rationality and knowledge
Run the GAMUT: A Comprehensive Approach to Evaluating Game-Theoretic Algorithms
AAMAS '04 Proceedings of the Third International Joint Conference on Autonomous Agents and Multiagent Systems - Volume 2
Computing pure nash equilibria in graphical games via markov random fields
EC '06 Proceedings of the 7th ACM conference on Electronic commerce
Memetic networks: analyzing the effects of network properties in multi-agent performance
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 1
A study on the stability and efficiency of graphical games with unbounded treewidth
Proceedings of the 2013 international conference on Autonomous agents and multi-agent systems
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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.