Dynamics in network interaction games

Abstract

We study the convergence times of dynamics in games involving graphical relationships of players. Our model of local interaction games generalizes a variety of recently studied games in game theory and distributed computing. In a local interaction game each agent is a node embedded in a graph and plays the same 2-player game with each neighbor. He can choose his strategy only once and must apply his choice in each game he is involved in. This represents a fundamental model of decision making with local interaction and distributed control. Furthermore, we introduce a generalization called 2-type interaction games, in which one 2-player game is played on edges and possibly another game is played on non-edges. For the popular case with symmetric 2 ×2 games, we show that several dynamics converge in polynomial time. This includes arbitrary sequential better response dynamics, as well as concurrent dynamics resulting from a distributed protocol that does not rely on global knowledge. We supplement these results with an experimental comparison of sequential and concurrent dynamics. © 2009 Springer Berlin Heidelberg.