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Mean Field Games on Prosumers

Author

Listed:
  • Wouter Baar

    (University of Groningen)

  • Dario Bauso

    (University of Groningen
    Università di Palermo)

Abstract

In the realm of dynamic demand, prosumers are agents that can produce and consume goods. In this paper, the problem we address involves a large population of prosumers and each prosumer has to decide if (s)he wants to produce or consume a certain amount of goods. The strategy of each agent depends on the average behavior of the population. We set the problem in a game-theoretic framework by modeling every prosumer as a player. For every player, a cost functional is designed to incentivize cooperation among the players. By taking the population size very large, a mean field game arises. The contributions of this paper are as follows. Firstly, we formulate the problem as first-order and second-order mean field games, the latter arises when we take stochastic disturbances into account. Secondly, mean field equilibria are derived by studying the corresponding linear-quadratic optimal control problem. Thirdly, results on stability of the first-order and second-order equilibria are established. A numerical study covering our findings concludes the paper.

Suggested Citation

  • Wouter Baar & Dario Bauso, 2022. "Mean Field Games on Prosumers," SN Operations Research Forum, Springer, vol. 3(4), pages 1-27, December.
    • Handle: RePEc:spr:snopef:v:3:y:2022:i:4:d:10.1007_s43069-022-00164-6
    DOI: 10.1007/s43069-022-00164-6
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    References listed on IDEAS

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    1. Fabio Bagagiolo & Dario Bauso, 2014. "Mean-Field Games and Dynamic Demand Management in Power Grids," Dynamic Games and Applications, Springer, vol. 4(2), pages 155-176, June.
    2. Diogo Gomes & João Saúde, 2014. "Mean Field Games Models—A Brief Survey," Dynamic Games and Applications, Springer, vol. 4(2), pages 110-154, June.
    3. Michel Benaim & Josef Hofbauer & Sylvain Sorin, 2005. "Stochastic Approximations and Differential Inclusions II: Applications," Levine's Bibliography 784828000000000098, UCLA Department of Economics.
    4. Michel Benaïm & Josef Hofbauer & Sylvain Sorin, 2005. "Stochastic Approximations and Differential Inclusions; Part II: Applications," Working Papers hal-00242974, HAL.
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    Cited by:

    1. Bożena Gajdzik & Magdalena Jaciow & Radosław Wolniak & Robert Wolny & Wieslaw Wes Grebski, 2023. "Energy Behaviors of Prosumers in Example of Polish Households," Energies, MDPI, vol. 16(7), pages 1-26, March.

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