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Generalizing the basic idea of Ma et al. (2015), we argue that the frontier of the LOB (e.g., the best asking price) is the value function of a mean-field stochastic control ON MEAN FIELD GAMES Pierre-Louis LIONS Coll`ege de France, Paris (joint project with Jean-Michel LASRY) 2012 SIAM Annual Meeting, Minneapolis, USA July 12, 2012 Pierre-Louis LIONS Coll`ege de France, Paris (joint project with Jean-Michel LASRY)ON MEAN FIELD GAMES Mean field game theory is devoted to the analysis of differential games with infinitely many players. For such large population dynamic games, it is unrealistic for a player to collect detailed state information about all other players. Fortunately this impossible task is useless: mean field game theory explains that for stationary mean-field games.

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However, this need not always be the case: in a variant of mean-field theory called dynamical mean-field theory (DMFT), the mean field becomes a time-dependent quantity. 其中 mean field term 可以看作一个参数。此时可以证明 is optimal control, i.e., 现在，我们把 Mean field game 问题转化为了一个耦合偏微分方程组 (HJB-FP system) with and . 对于 mean field game problem, the pair is the solution. Approximation of Nash games with a large number of players Mean eld game theory is devoted to the analysis of di erential games with in nitely many players. For such large population dynamic games, it is unrealistic for a player to collect detailed state information about all other players. Fortunately this impossible task is Mean Field Games, which models the the dynamics of large number of agents, has applications in many areas such as economics, finance, dynamics of crowds as well as in biology and and social sciences. The starting point is the analysis of N-player differential games when N tends to infinity.

In the game theory and stochas-tic control literature, there are two very closely related modeling frameworks that are referred to as mean-field games andstationary mean-field games. We highlight the difference between these two modeling frameworks in Sec. 5.2. The current literature on using These game situations, also referred to as mean-field-type games, involve novel equilibrium systems to be solved.

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2019-05-30 · This paper proposes a posterior sampling based approach for reinforcement learning in the mean-field game, where each agent samples a transition probability from the previous transitions. We show that the policy and action distributions converge to the optimal oblivious strategy and the limiting distribution, respectively, which constitute an MFE. Notes on Mean Field Games (from P.-L.

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They study strategic decision making in large populations where the individuals interact via certain mean-field quantities. The ground metrics and running costs of the games are of essential importance but are often unknown or only partially known. In this paper, we propose mean-field game inverse Mean Field Multi-Agent Reinforcement Learning.

M. Huang. "A mean field capital accumulation game with HARA utility". Dynamic Games and Applications: special issue on mean field games, vol. 3, pp. 446-472, 2013 . Mean-field game theory is the study of strategic decision making by small interacting agents in very large populations. Use of the term "mean field" is inspired by mean-field theory in physics, which considers the behaviour of systems of large numbers of particles where individual particles have negligible impact upon the system.
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Gomes, D., Mohr, J., Sousa, R.: Discrete time, finite state space mean field games. Mean Field Game (MFG) theory studies the existence of Nash equilibria, together with the individual strategies which generate them, in games involving a large number of agents modeled by controlled stochastic dynamical systems. This article discusses the interaction between economic growth in the sense of human capital accumulation and the dynamics of inequalities.

MEAN FIELD GAMES: A TOY MODEL ON AN ERDOS-RENYI GRAPH.
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Abstract. The purpose of this short article is to address a simple ex-ample of a game with a large number of players in mean eld interaction Minyi HuangCarleton University, Canada Mean Field Games in Economics Y. Achdou (LJLL, Universit e Paris-Diderot) June, 2019 | CIME, Cetraro Y. Achdou Mean eld games Prof. Wilfrid Gangbo from UCLA gave a talk entitled "On a Mean Field Game equation I" at Optimal Control and PDE of the Tohoku Forum for Creativity, Tohoku U for stationary mean-field games. In the game theory and stochas-tic control literature, there are two very closely related modeling frameworks that are referred to as mean-field games andstationary mean-field games.