Network Threshold Games

TL;DR

This paper introduces a novel approach to analyze threshold games on networks with heterogeneous thresholds by transforming the network, linking equilibria to k-cores, and demonstrating stability in linear-quadratic preference settings.

Contribution

It develops a network transformation method to analyze heterogeneous threshold games and characterizes equilibria using k-cores, extending existing models.

Findings

Equilibria are characterized by the k-core of the transformed network.

The model generalizes the Ballester et al. (2006) framework to binary actions.

The equilibrium is stable regardless of move order in linear-quadratic preferences.

Abstract

This paper proposes a new lens for studying threshold games played on networks when the thresholds are heterogeneous. These are games where agents have two possible actions, and prefer action 1 if and only if enough of their neighbours choose action 1. We propose a transformation of the network that `absorbs' the heterogeneity in thresholds into the network. This allows us to characterise equilibria in terms of the k-core -- a well-studied measure of network cohesiveness -- of the transformed network. Our model is also the direct analogy to the workhorse model of Ballester et al. (2006) when actions are 0 or 1. Further, our binary action version exhibits a remarkable stability property. When agents have linear-quadratic preferences, the k-core of the transformed network characterises the unique subgame perfect equilibrium of a sequential move version of the game -- no matter what order agents move in.