On non-uniqueness in mean field games

DOI10.1090/proc/15046zbMath1444.91025arXiv1908.06207OpenAlexW3006282686MaRDI QIDQ3298177

Xin Zhang, Erhan Bayraktar

Publication date: 21 July 2020

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1908.06207

zbMATH Keywords

entropy solutionNash equilibriumnon-uniquenessmaster equationmean field game

Mathematics Subject Classification ID

Mean field games (aspects of game theory) (91A16)

Related Items (12)

Selection by vanishing common noise for potential finite state mean field games ⋮ Finite state mean field games with Wright-Fisher common noise ⋮ Linear-quadratic mean field games of controls with non-monotone data ⋮ Generic properties of first-order mean field games ⋮ Control theory approach to continuous-time finite state mean field games ⋮ Polarization and coherence in mean field games driven by private and social utility ⋮ Dynamic Cournot-Nash equilibrium: the non-potential case ⋮ Propagation of chaos of forward-backward stochastic differential equations with graphon interactions ⋮ Selected topics in mean field games ⋮ Optimal Policies for Convex Symmetric Stochastic Dynamic Teams and their Mean-Field Limit ⋮ Solvability of infinite horizon McKean-Vlasov FBSDEs in mean field control problems and games ⋮ Finite State Mean Field Games with Wright–Fisher Common Noise as Limits ofN-Player Weighted Games

Cites Work

• Continuous time finite state mean field games
• Mean field games. I: The stationary case
• Mean field games. II: Finite horizon and optimal control
• Mean field games
• Convergence, fluctuations and large deviations for finite state mean field games via the master equation
• Selection of equilibria in a linear quadratic mean-field game
• Large population stochastic dynamic games: closed-loop McKean-Vlasov systems and the Nash certainty equivalence principle
• Socio-economic applications of finite state mean field games
• The Master Equation and the Convergence Problem in Mean Field Games
• Analysis of a Finite State Many Player Game Using Its Master Equation
• On the Convergence Problem in Mean Field Games: A Two State Model without Uniqueness
• Large-Population Cost-Coupled LQG Problems With Nonuniform Agents: Individual-Mass Behavior and Decentralized $\varepsilon$-Nash Equilibria
• Probabilistic Theory of Mean Field Games with Applications I
• Probabilistic Theory of Mean Field Games with Applications II

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