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Dynamic Games with Strategic Complements and Large Number of Players

Author

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  • Stefanny Ramirez

    (University of Groningen)

  • Dario Bauso

    (University of Groningen
    Università di Palermo)

Abstract

We study dynamic games with strategic complements where each player is modeled by a scalar flow dynamical system with a controlled input and an uncontrolled output. The model originates in inventory control problems with shared set-up costs and a large number of players. An activation cost is shared among active players, namely players who control their dynamics at a given time. As a main contribution, we prove that two-threshold strategies, like the (s, S) strategies used in inventory control, are mean-field equilibrium strategies in dynamic games with a large number of players. Furthermore, we provide conditions for the convergence of the nonstationary mean-field equilibrium to the stationary one in the limit.

Suggested Citation

  • Stefanny Ramirez & Dario Bauso, 2023. "Dynamic Games with Strategic Complements and Large Number of Players," Journal of Optimization Theory and Applications, Springer, vol. 197(1), pages 1-21, April.
    • Handle: RePEc:spr:joptap:v:197:y:2023:i:1:d:10.1007_s10957-023-02174-8
    DOI: 10.1007/s10957-023-02174-8
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    References listed on IDEAS

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    1. Andrew J. Clark & Herbert Scarf, 2004. "Optimal Policies for a Multi-Echelon Inventory Problem," Management Science, INFORMS, vol. 50(12_supple), pages 1782-1790, December.
    2. Antonio Cabrales & Piero Gottardi & Fernando Vega-Redondo, 2017. "Risk Sharing and Contagion in Networks," The Review of Financial Studies, Society for Financial Studies, vol. 30(9), pages 3086-3127.
    3. Diogo Gomes & João Saúde, 2014. "Mean Field Games Models—A Brief Survey," Dynamic Games and Applications, Springer, vol. 4(2), pages 110-154, June.
    4. Dario Bauso & Quanyan Zhu & Tamer Başar, 2016. "Decomposition and Mean-Field Approach to Mixed Integer Optimal Compensation Problems," Journal of Optimization Theory and Applications, Springer, vol. 169(2), pages 606-630, May.
    5. Matthew Elliott & Benjamin Golub & Matthew O. Jackson, 2014. "Financial Networks and Contagion," American Economic Review, American Economic Association, vol. 104(10), pages 3115-3153, October.
    6. Juan Carlos González-Avella & Victor M Eguíluz & Matteo Marsili & Fernado Vega-Redondo & Maxi San Miguel, 2011. "Threshold Learning Dynamics in Social Networks," PLOS ONE, Public Library of Science, vol. 6(5), pages 1-9, May.
    7. Bauso, Dario & Giarré, Laura & Pesenti, Raffaele, 2009. "Distributed consensus in noncooperative inventory games," European Journal of Operational Research, Elsevier, vol. 192(3), pages 866-878, February.
    8. Stefanny Ramirez & Dario Bauso, 2021. "Dynamic Coordination Games with Activation Costs," Dynamic Games and Applications, Springer, vol. 11(3), pages 580-596, September.
    9. Sachin Adlakha & Ramesh Johari, 2013. "Mean Field Equilibrium in Dynamic Games with Strategic Complementarities," Operations Research, INFORMS, vol. 61(4), pages 971-989, August.
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