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Network Threshold Games

Author

Listed:
  • Langtry, A.
  • Taylor, S.
  • Zhang, Y.

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.

Suggested Citation

  • Langtry, A. & Taylor, S. & Zhang, Y., 2026. "Network Threshold Games," Cambridge Working Papers in Economics 2633, Faculty of Economics, University of Cambridge.
    • Handle: RePEc:cam:camdae:2633
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    JEL classification:

    • D85 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Network Formation
    • O33 - Economic Development, Innovation, Technological Change, and Growth - - Innovation; Research and Development; Technological Change; Intellectual Property Rights - - - Technological Change: Choices and Consequences; Diffusion Processes

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