Fuzzy Conventions

TL;DR

This paper analyzes how network structure influences equilibrium outcomes in binary coordination games with random utility, revealing that different networks lead to varying sets of possible average behaviors, including a novel risk dominance concept.

Contribution

It introduces a new understanding of fuzzy equilibria in networked coordination games and characterizes how network topology affects equilibrium sets.

Findings

Complete graphs maximize the set of equilibrium behaviors.

Lattice networks restrict the equilibrium set to a single outcome.

A new version of risk dominance is proposed for games with random utility.

Abstract

We study binary coordination games with random utility played in networks. A typical equilibrium is fuzzy -- it has positive fractions of agents playing each action. The set of average behaviors that may arise in an equilibrium typically depends on the network. The largest set (in the set inclusion sense) is achieved by a network that consists of a large number of copies of a large complete graph. The smallest set (in the set inclusion sense) is achieved on a lattice-type network. It consists of a single outcome that corresponds to a novel version of risk dominance that is appropriate for games with random utility.