Network Threshold Games

Alastair Langtry, Sarah Taylor and Yifan Zhang

Cambridge Working Papers in Economics from Faculty of Economics, University of Cambridge

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.

Keywords: Networks; Threshold Games; Strategic Complements; Contagion; Diffusion; Coordination (search for similar items in EconPapers)
JEL-codes: D85 O33 (search for similar items in EconPapers)
Date: 2026-04-17
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Persistent link: https://EconPapers.repec.org/RePEc:cam:camdae:2633

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