A Probabilistic Approach to Extended Finite State Mean Field Games

René Carmona () and Peiqi Wang ()
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René Carmona: Department of Operations Research and Financial Engineering, Princeton University, Princeton, New Jersey 08544
Peiqi Wang: Bank of America, New York, New York 10281

Mathematics of Operations Research, 2021, vol. 46, issue 2, 471-502

Abstract: We develop a probabilistic approach to continuous-time finite state mean field games. Based on an alternative description of continuous-time Markov chains by means of semimartingales and the weak formulation of stochastic optimal control, our approach not only allows us to tackle the mean field of states and the mean field of control at the same time, but also extends the strategy set of players from Markov strategies to closed-loop strategies. We show the existence and uniqueness of Nash equilibrium for the mean field game as well as how the equilibrium of a mean field game consists of an approximative Nash equilibrium for the game with a finite number of players under different assumptions of structure and regularity on the cost functions and transition rate between states.

Keywords: Primary: 49N80; secondary: 90C40; Primary: Games/group decisions: stochastic; secondary: dynamic programming/optimal control: Markov: finite state; mean field games; finite state space; weak formulation of optimal control; approximative Nash equilibrium; McKean–Vlasov BSDE (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormoor:v:46:y:2021:i:2:p:471-502

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