Graphical Models for Game Theory
UAI '01 Proceedings of the 17th Conference in Uncertainty in Artificial Intelligence
Nash equilibria in graphical games on trees revisited
EC '06 Proceedings of the 7th ACM conference on Electronic commerce
On the Impact of Combinatorial Structure on Congestion Games
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Computing good nash equilibria in graphical games
Proceedings of the 8th ACM conference on Electronic commerce
Computing Equilibria in Anonymous Games
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Symmetries and the complexity of pure Nash equilibrium
Journal of Computer and System Sciences
Dynamic restriction of choices: a preliminary logical report
Proceedings of the 12th Conference on Theoretical Aspects of Rationality and Knowledge
Stability under Strategy Switching
CiE '09 Proceedings of the 5th Conference on Computability in Europe: Mathematical Theory and Computational Practice
Strategies in games: a logic-automata study
ESSLLI'10 Proceedings of the 2010 conference on ESSLLI 2010, and ESSLLI 2011 conference on Lectures on Logic and Computation
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We study repeated normal form games where the number of players is large and suggest that it is useful to consider a neighbourhood structure on the players. The structure is given by a graph G whose nodes are players and edges denote visibility. The neighbourhoods are maximal cliques in G. The game proceeds in rounds where in each round the players of every clique X of G play a strategic form game among each other. A player at a node v strategises based on what she can observe, i.e., the strategies and the outcomes in the previous round of the players at vertices adjacent to v. Based on this, the player may switch strategies in the same neighbourhood, or migrate to another neighbourhood. Player types, giving the rationale for such switching, are specified in a simple modal logic. We show that given the initial neighbourhood graph and the types of the players in the logic, we can effectively decide if the game eventually stabilises. We then prove a characterisation result for these games for arbitrary types using potentials. We then offer some applications to the special case of weighted co-ordination games where we can compute bounds on how long it takes to stabilise.