# Consensus and Information Cascades in Game-Theoretic Imitation Dynamics with Static and Dynamic Network Topologies

## TL;DR

This paper models strategic imitation in networks, analyzing convergence to consensus and the impact of network topology changes, with applications to trend spreading and information cascades.

## Contribution

It introduces a new model of strategic imitation on arbitrary networks, including dynamic topologies, and analyzes convergence and trend spreading phenomena.

## Key findings

- Consensus convergence under certain conditions
- Network topology evolves to disconnected cliques in prisoner's dilemma
- Empirical results support trend-spreading model

## 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.