Nonlocal Bertrand and Cournot mean field games with general nonlinear demand schedule

Graber, P. Jameson; Ignazio, Vincenzo; Neufeld, Ariel

doi:10.1016/j.matpur.2021.02.002

Cited by 10 publications

(2 citation statements)

References 24 publications

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“…Þ¼0. The solution of system ( 21) is related to the solution of system (22). This paper only solves a particular class of equilibrium solutions: the equilibrium point when time t approaches infinity.…”

Section: Mean Field Gamementioning

confidence: 99%

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Stability of a mean field game of production adjustment

Wang

Xin

2023

Asian Journal of Control

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We propose a mean field game model to study the stability of production adjustment by extending a kind of linear quadratic Gaussian game in large population systems. First, we present the model's equilibrium solutions by a backward HJB equation and a forward FPK equation. Second, we employ the local perturbation method to transform the nonlinear problem into a linear one to study the solutions' stability. Third, we use the spectrum and contraction analyses to study the stationary solutions' linear stability. At last, we validate the results by the numerical simulation. The results show that the additional cost coefficient and noise intensity affect the system's stability. If the additional cost coefficient and the noise intensity are large enough for firms to change their outputs, then firms will try to reduce their production adjustment and remain stable long‐term.

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Section: Mean Field Gamementioning

confidence: 99%

“…When the number of firms tends to be infinite, the ordinary differential game is no longer applicable [19,20]. We can consider using a mean field game [21][22][23] to solve this problem.…”

Section: Introductionmentioning

confidence: 99%

Stability of a mean field game of production adjustment

Wang

Xin

2023

Asian Journal of Control

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Weak solutions for potential mean field games of controls

Graber

Mullenix

Pfeiffer

2021

Nonlinear Differ. Equ. Appl.

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In this expository article, we give an overview of the concept of potential mean field games of first order. We give a new proof that minimizers of the potential are equilibria by using a Lagrangian formulation. We also provide criteria to determine whether or not a game has a potential. Finally, we discuss in some depth the selection problem in mean field games, which consists in choosing one out of multiple Nash equilibria.

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Mean field games with monotonous interactions through the law of states and controls of the agents

Kobeissi

2022

Nonlinear Differ. Equ. Appl.

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Nonlocal Bertrand and Cournot mean field games with general nonlinear demand schedule

Cited by 10 publications

References 24 publications

Stability of a mean field game of production adjustment

Stability of a mean field game of production adjustment

Weak solutions for potential mean field games of controls

Mean field games with monotonous interactions through the law of states and controls of the agents

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