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A Variational Approach to Network Games

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  • Melo, Emerson

Abstract

This paper studies strategic interaction in networks. We focus on games of strategic substitutes and strategic complements, and departing from previous literature, we do not assume particular functional forms on players' payoffs. By exploiting variational methods, we show that the uniqueness, the comparative statics, and the approximation of a Nash equilibrium are determined by a precise relationship between the lowest eigenvalue of the network, a measure of players' payoff concavity, and a parameter capturing the strength of the strategic interaction among players. We apply our framework to the study of aggregative network games, games of mixed interactions, and Bayesian network games.

Suggested Citation

  • Melo, Emerson, 2018. "A Variational Approach to Network Games," ETA: Economic Theory and Applications 268732, Fondazione Eni Enrico Mattei (FEEM).
    • Handle: RePEc:ags:feemth:268732
    DOI: 10.22004/ag.econ.268732
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    Cited by:

    1. Shi, Xiangyu, 2024. "Helping behavior in networked organizations," European Economic Review, Elsevier, vol. 165(C).
    2. Allouch, Nizar & King, Maia, 2021. "Welfare targeting in networks," Journal of Mathematical Economics, Elsevier, vol. 96(C).
    3. Luke A. Boosey & Christopher Brown, 2021. "Contests with Network Externalities: Theory & Evidence," Working Papers wp2021_07_02, Department of Economics, Florida State University.
    4. Nizar Allouch & Maia King, 2019. "Constrained public goods in networks," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 21(5), pages 895-902, October.
    5. Parise, Francesca & Ozdaglar, Asuman, 2019. "A variational inequality framework for network games: Existence, uniqueness, convergence and sensitivity analysis," Games and Economic Behavior, Elsevier, vol. 114(C), pages 47-82.
    6. Hu, Xiaowei & Li, Peng, 2022. "Relief and stimulus in a cross-sector multi-product scarce resource supply chain network," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 168(C).
    7. Emerson Melo, 2022. "On the uniqueness of quantal response equilibria and its application to network games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 74(3), pages 681-725, October.
    8. Xiaowei Hu & Peng Li, 2021. "Relief and Stimulus in A Cross-sector Multi-product Scarce Resource Supply Chain Network," Papers 2101.09373, arXiv.org, revised Nov 2022.

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    Keywords

    Research Methods/ Statistical Methods;

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