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A Variational Approach to Network Games

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  • Emerson Melo

    (Indiana University, Department of Economics)

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

  • Emerson Melo, 2018. "A Variational Approach to Network Games," Working Papers 2018.05, Fondazione Eni Enrico Mattei.
    • Handle: RePEc:fem:femwpa:2018.05
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    References listed on IDEAS

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    Cited by:

    1. 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.
    2. Allouch, Nizar & King, Maia, 2021. "Welfare targeting in networks," Journal of Mathematical Economics, Elsevier, vol. 96(C).
    3. 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.
    4. 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.
    5. 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.
    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. Luke A. Boosey & Christopher Brown, 2021. "Contests with Network Externalities: Theory & Evidence," Working Papers wp2021_07_02, Department of Economics, Florida State University.

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    More about this item

    Keywords

    Network Games; Variational Inequalities; Lowest Eigenvalue; Shock Propagation;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D85 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Network Formation
    • H41 - Public Economics - - Publicly Provided Goods - - - Public Goods
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium

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