Convergence to equilibrium in local interaction games

Authors:
Andrea Montanari;Amin Saberi
Affiliations:
Departments of Electrical Engineering and Statistics, Stanford University;Department of Management Science and Engineering, Stanford University
Venue:
ACM SIGecom Exchanges
Year:
2009

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Abstract

We study a simple game-theoretic model for the spread of an innovation in a network. The diffiusion of the innovation is modeled as the dynamics of a coordination game in which the adoption of a common strategy between players has a higher payoff. Classical results in game theory provide a simple condition for the innovation to spread through the network. The present paper characterizes the rate of convergence as a function of graph structure. In particular, we derive a dichotomy between well-connected (e.g. random) graphs that show slow convergence and poorly connected, low dimensional graphs that show fast convergence.