Mean Field Games on Prosumers

Wouter Baar () and Dario Bauso ()
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Wouter Baar: University of Groningen
Dario Bauso: University of Groningen

SN Operations Research Forum, 2022, vol. 3, issue 4, 1-27

Abstract: 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.

Keywords: Mean field games; Dynamic demand; Prosumers; Best response (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s43069-022-00164-6

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