Consensus and information cascades in game-theoretic imitation dynamics with static and dynamic network topologies

Research output: Contribution to journalArticle

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 the 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.

Original languageEnglish (US)
Pages (from-to)597-628
Number of pages32
JournalSIAM Journal on Applied Dynamical Systems
Volume18
Issue number2
DOIs
StatePublished - Jan 1 2019

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Imitation
Dynamic Networks
Network Topology
Cascade
Topology
Game
Clique
Matrix Game
Converge
Prisoners' Dilemma
Difference equations
Model
Difference equation
Social Networks
Discrete-time
Choose
Update
Arbitrary
Graph in graph theory
Trends

All Science Journal Classification (ASJC) codes

  • Analysis
  • Modeling and Simulation

Cite this

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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 the 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.",
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