Consensus and Information Cascades in Game-Theoretic Imitation Dynamics with Static and Dynamic Network Topologies
arXiv:1903.11429 · doi:10.1137/16M109675X
Abstract
We construct a model of strategic imitation in an arbitrary network of players who interact through an additive game. Assuming a discrete time update, we show a condition under which the resulting difference equations converge to consensus. Two conjectures on general convergence are also discussed. We then consider the case where players not only may choose their strategies, but also affect their local topology. We show that for prisoner's dilemma, the graph structure converges to a set of disconnected cliques and strategic consensus occurs in each clique. Several examples from various matrix games are provided. A variation of the model is then used to create a simple model for the spreading of trends, or information cascades in (e.g., social) networks. We provide theoretical and empirical results on the trend-spreading model.
arXiv comment30 pages, 15 figures, Accepted to SIAM J. Applied Dynamical Systems
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