Related papers: Some remarks on Mean Field Games
The celebrated Krusel-Smith growth model is an important example of a Mean Field Game with a common noise. The Mean Field Game is encoded in the master equation, a partial differential equation satisfied by the value of the game which…
The goal of the paper is to introduce a formulation of the mean field game with major and minor players as a fixed point on a space of controls. This approach emphasizes naturally the role played by McKean-Vlasov dynamics in some of the…
Using the Minority Game model we study a broad spectrum of problems of market mechanism. We study the role of different types of agents: producers, speculators as well as noise traders. The central issue here is the information flow :…
In this paper we study a class of matrix-valued linear-quadratic mean-field-type games for both the risk-neutral, risk-sensitive and robust cases. Non-cooperation, full cooperation and adversarial between teams are treated. We provide a…
In this paper, we propose a mean-field game model for the price formation of a commodity whose production is subjected to random fluctuations. The model generalizes existing deterministic price formation models. Agents seek to minimize…
Mean field games (MFGs) are a promising framework for modeling the behavior of large-population systems. However, solving MFGs can be challenging due to the coupling of forward population evolution and backward agent dynamics. Typically,…
The theory of mean field games is a tool to understand noncooperative dynamic stochastic games with a large number of players. Much of the theory has evolved under conditions ensuring uniqueness of the mean field game Nash equilibrium.…
We present a simple game model where agents with different memory lengths compete for finite resources. We show by simulation and analytically that an instability exists at a critical memory length, and as a result, different memory lengths…
In this note we prove the uniqueness of solutions to a class of Mean Field Games systems subject to possibly degenerate individual noise. Our results hold true for arbitrary long time horizons and for general non-separable Hamiltonians that…
We investigate an infinite-horizon time-inconsistent mean-field game (MFG) in a discrete time setting. We first present a classic equilibrium for the MFG and its associated existence result. This classic equilibrium aligns with the…
In a situation of moral hazard, this paper investigates the problem of Principal with $n$ Agents when the number of Agents $n$ goes to infinity. There is competition between the Agents expressed by the fact that they optimize their utility…
We introduce a notion of weak solution of the master equation without idiosyncratic noise in Mean Field Game theory and establish its existence, uniqueness up to a constant and consistency with classical solutions when it is smooth. We work…
This paper establishes unique solvability of a class of Graphon Mean Field Game equations. The special case of a constant graphon yields the result for the Mean Field Game equations.
The policy iteration method is a classical algorithm for solving optimal control problems. In this paper, we introduce a policy iteration method for Mean Field Games systems, and we study the convergence of this procedure to a solution of…
Mean Field Games (MFG) theory describes strategic interactions in differential games with a large number of small and indistinguishable players. Traditionally, the players' control impacts only the drift term in the system's dynamics,…
When controlling multi-agent systems, the trade-off between performance and scalability is a major challenge. Here, we address this difficulty by using mean field games (MFGs), which is a framework that deduces the macroscopic dynamics…
We introduce a mean-field term to an evolutionary spatial game model. Namely, we consider the game of Nowak and May, based on the Prisoner's dilemma, and augment the game rules by a self-consistent mean-field term. This way, an agent…
The recently developed mean-field game models of corruption and bot-net defence in cyber-security, the evolutionary game approach to inspection and corruption, and the pressure-resistance game element, can be combined under an extended…
In mix-game which is an extension of minority game, there are two groups of agents; group1 plays the majority game, but the group2 plays the minority game. This paper studies the change of the average winnings of agents and volatilities vs.…
A simple model of corruption that takes into account the effect of the interaction of a large number of agents by both rational decision making and myopic behavior is developed. Its stationary version turns out to be a rare example of an…