Network Threshold Games
Alastair Langtry, Sarah Taylor, Yifan Zhang · RePEc: Research Papers in Economics · 2024
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.