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arXiv · 2406.04540

Network Threshold Games

Alastair Langtry·Sarah Taylor·Yifan Zhang
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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.

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Alastair Langtry, Sarah Taylor, Yifan Zhang. 2025-08-06. Network Threshold Games. https://arxiv.org/abs/2406.04540

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