IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2406.04540.html
   My bibliography  Save this paper

Network Threshold Games

Author

Listed:
  • Alastair Langtry
  • Sarah Taylor
  • Yifan Zhang

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

  • Alastair Langtry & Sarah Taylor & Yifan Zhang, 2024. "Network Threshold Games," Papers 2406.04540, arXiv.org, revised Aug 2025.
    • Handle: RePEc:arx:papers:2406.04540
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2406.04540
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-180, January.
    2. Frank M. Bass, 1969. "A New Product Growth for Model Consumer Durables," Management Science, INFORMS, vol. 15(5), pages 215-227, January.
    3. Jackson, Matthew O. & Zenou, Yves, 2015. "Games on Networks," Handbook of Game Theory with Economic Applications,, Elsevier.
    4. Julien Gagnon & Sanjeev Goyal, 2017. "Networks, Markets, and Inequality," American Economic Review, American Economic Association, vol. 107(1), pages 1-30, January.
    5. Bernheim, B. Douglas & Peleg, Bezalel & Whinston, Michael D., 1987. "Coalition-Proof Nash Equilibria I. Concepts," Journal of Economic Theory, Elsevier, vol. 42(1), pages 1-12, June.
    6. Morris, Stephen & Ui, Takashi, 2004. "Best response equivalence," Games and Economic Behavior, Elsevier, vol. 49(2), pages 260-287, November.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Dubey, Pradeep & Haimanko, Ori & Zapechelnyuk, Andriy, 2006. "Strategic complements and substitutes, and potential games," Games and Economic Behavior, Elsevier, vol. 54(1), pages 77-94, January.
    2. Jacques Durieu & Hans Haller & Nicolas Querou & Philippe Solal, 2008. "Ordinal Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 10(02), pages 177-194.
    3. Belleflamme, Paul, 2000. "Stable Coalition Structures with Open Membership and Asymmetric Firms," Games and Economic Behavior, Elsevier, vol. 30(1), pages 1-21, January.
    4. Kukushkin, Nikolai S., 2015. "Cournot tatonnement and potentials," Journal of Mathematical Economics, Elsevier, vol. 59(C), pages 117-127.
    5. Shinohara, Ryusuke, 2019. "Undominated coalition-proof Nash equilibria in quasi-supermodular games with monotonic externalities," Economics Letters, Elsevier, vol. 176(C), pages 86-89.
    6. Newton, Jonathan, 2012. "Coalitional stochastic stability," Games and Economic Behavior, Elsevier, vol. 75(2), pages 842-854.
    7. Paul Milgrom & John Roberts, "undated". "Strongly Coalition-Proof Equilibria in Games with Strategic Complementarities," Working Papers 95002, Stanford University, Department of Economics.
    8. Ui, Takashi, 2016. "Bayesian Nash equilibrium and variational inequalities," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 139-146.
    9. Attila Ambrus & Markus Mobius & Adam Szeidl, 2014. "Consumption Risk-Sharing in Social Networks," American Economic Review, American Economic Association, vol. 104(1), pages 149-182, January.
    10. Savvateev Alexey, 2003. "Strong equilibrium implementation for a principal with heterogeneous agents," EERC Working Paper Series 00-103e, EERC Research Network, Russia and CIS.
    11. Cao, Zhigang & Chen, Xujin & Qin, Cheng-Zhong & Wang, Changjun & Yang, Xiaoguang, 2018. "Embedding games with strategic complements into games with strategic substitutes," Journal of Mathematical Economics, Elsevier, vol. 78(C), pages 45-51.
    12. Segal, Ilya, 2003. "Coordination and discrimination in contracting with externalities: divide and conquer?," Journal of Economic Theory, Elsevier, vol. 113(2), pages 147-181, December.
    13. Zenou, Yves & Bochet, Olivier & Faure, Mathieu & Long, Yan, 2020. "Perceived Competition in Networks," CEPR Discussion Papers 15582, C.E.P.R. Discussion Papers.
    14. Yunke Mai & Bin Hu, 2023. "Optimizing Free-to-Play Multiplayer Games with Premium Subscription," Management Science, INFORMS, vol. 69(6), pages 3437-3456, June.
    15. UI, Takashi & 宇井, 貴志, 2015. "Bayesian Nash Equilibrium and Variational Inequalities," Discussion Papers 2015-08, Graduate School of Economics, Hitotsubashi University.
    16. Federico Quartieri & Ryusuke Shinohara, 2015. "Coalition-proofness in a class of games with strategic substitutes," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(4), pages 785-813, November.
    17. Francesco Feri & Paolo Pin, 2020. "Externalities Aggregation In Network Games," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 61(4), pages 1635-1658, November.
    18. Zenou, Yves & Chen, Ying-Ju & Zhou, Junjie, 2015. "Multiple Activities for Socially-Connected Criminals," CEPR Discussion Papers 10709, C.E.P.R. Discussion Papers.
    19. Belo, Rodrigo & Ferreira, Pedro, 2021. "Free Riding in Products with Positive Network Externalities: Empirical Evidence from a Large Mobile Network," SocArXiv wz4k9, Center for Open Science.
    20. Wedad Elmaghraby & P{i}nar Keskinocak, 2003. "Dynamic Pricing in the Presence of Inventory Considerations: Research Overview, Current Practices, and Future Directions," Management Science, INFORMS, vol. 49(10), pages 1287-1309, October.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2406.04540. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.