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Nash equilibria of networked games with delayed coupling in the high population regime

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  • Tamer Başar

    (University of Illinois)

Abstract

This paper considers a class of stochastic nonzero-sum discrete-time dynamic games with networked players where each player has its own state dynamics which has the states of other players also entering with, however, some time delay. This delayed coupling makes this a nonstandard class of games where the existing theory does not apply, particularly since the underlying information structure restricts the players to use only their local states in constructing their controls. What is sought is Nash equilibrium under such information structure when there is a high population of players. The paper introduces a general methodology within the mean-field framework, and applies it to games with linear dynamics and quadratic objective functions for some explicit characterization of the mean-field equilibrium, which is then used to obtain an approximate Nash equilibrium when there is a finite number of players. The approximate Nash equilibrium policies of the players turn out to be in the form of current local state feedback and some mean-field term generated by high-order dynamics.

Suggested Citation

  • Tamer Başar, 2025. "Nash equilibria of networked games with delayed coupling in the high population regime," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 33(2), pages 415-427, June.
    • Handle: RePEc:spr:cejnor:v:33:y:2025:i:2:d:10.1007_s10100-025-00967-y
    DOI: 10.1007/s10100-025-00967-y
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    References listed on IDEAS

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    1. Muhammad Aneeq uz Zaman & Erik Miehling & Tamer Başar, 2023. "Reinforcement Learning for Non-stationary Discrete-Time Linear–Quadratic Mean-Field Games in Multiple Populations," Dynamic Games and Applications, Springer, vol. 13(1), pages 118-164, March.
    2. Jun Moon & Tamer Başar, 2019. "Risk-Sensitive Mean Field Games via the Stochastic Maximum Principle," Dynamic Games and Applications, Springer, vol. 9(4), pages 1100-1125, December.
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