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In the context of simple finite-state discrete time systems, we introduce a generalization of mean field game solution, called correlated solution, which can be seen as the mean field game analogue of a correlated equilibrium. Our notion of solution is justified in two ways: We prove that correlated solutions arise as limits of exchangeable correlated equilibria in restricted (Markov open-loop) strategies for the underlying $N$-player games, and we show how to construct approximate $N$-player correlated equilibria starting from a correlated solution to the mean field game.
Mean field games are concerned with the limit of large-population stochastic differential games where the agents interact through their empirical distribution. In the classical setting, the number of players is large but fixed throughout the game. Ho
This paper considers mean field games in a multi-agent Markov decision process (MDP) framework. Each player has a continuum state and binary action, and benefits from the improvement of the condition of the overall population. Based on an infinite ho
This paper studies Mean Field Games with a common noise given by a continuous time Markov chain under a Quadratic cost structure. The theory implies that the optimal path under the equilibrium is a Gaussian process conditional on the common noise. In
This paper studies an asymptotic solvability problem for linear quadratic (LQ) mean field games with controlled diffusions and indefinite weights for the state and control in the costs. We employ a rescaling approach to derive a low dimensional Ricca
We propose a mean field game model to study the question of how centralization of reward and computational power occur in the Bitcoin-like cryptocurrencies. Miners compete against each other for mining rewards by increasing their computational power.