Abstract

We analyze dynamic local interaction in population games where the local interaction structure (modeled as a graph) can change over time: A stochastic process generates a random sequence of graphs. This contrasts with models where the initial interaction structure (represented by a deterministic graph or the realization of a random graph) cannot change over time.

Highlights

  • Interaction in an economic, social, political or computational context is often local in the sense that it consists of pairwise interactions between neighbors

  • We find that if the support of the underlying random graph consists of all circular graphs, at least one player chose the risk dominant action initially, and updating is simultaneous, contagion with respect to the risk dominant action occurs

  • We find that when the evolution of the interaction structure is based on a binomial random graph, with probability one, contagion occurs

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Summary

Introduction

Interaction in an economic, social, political or computational context is often local in the sense that it consists of pairwise interactions between neighbors. Q.E.D. In the deterministic case (with a fixed interaction structure of the form V β , say) when action X is risk dominant and N is even, convergence to a two-cycle occurs. (i.e., θ > 1/n), with positive probability contagion with respect to action Y occurs even when a vast majority of the players initially chooses action X—and even when X is risk dominant.

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