Related papers: Regularity of the Value Function in Discounted Inf…

In this paper, we study a class of zero-sum two-player stochastic differential games with the controlled stochastic differential equations and the payoff/cost functionals of recursive type. As opposed to the pioneering work by Fleming and…

We propose a new approach to mean field games with major and minor players. Our formulation involves a two player game where the optimization of the representative minor player is standard while the major player faces an optimization over…

In this paper, we provide an effective characterization of all the subgame-perfect equilibria in infinite duration games played on finite graphs with mean-payoff objectives. To this end, we introduce the notion of requirement, and the…

This paper studies a discrete-time major-minor mean field game of stopping where the major player can choose either an optimal control or stopping time. We look for the relaxed equilibrium as a randomized stopping policy, which is…

We consider concurrent mean-payoff games, a very well-studied class of two-player (player 1 vs player 2) zero-sum games on finite-state graphs where every transition is assigned a reward between 0 and 1, and the payoff function is the…

The mean field games system is a coupled pair of nonlinear partial differential equations arising in differential game theory, as a limit as the number of agents tends to infinity. We prove existence and uniqueness of classical solutions…

Designing suitable reward functions for numerous interacting intelligent agents is challenging in real-world applications. Inverse reinforcement learning (IRL) in mean field games (MFGs) offers a practical framework to infer reward…

This paper is concerned with a backward-forward stochastic differential equation (BFSDE) system, in which a large number of negligible agents are coupled in their dynamics via state average. Here some BSDE is introduced as the dynamics of…

This paper investigates open-loop and feedback solutions of linear quadratic mean field (MF) games with a leader and a large number of followers. The leader first gives its strategy and then all the followers cooperate to optimize the…

We show that if either the process is strong Feller and the boundary point is probabilistically regular for the stopping set, or the process is strong Markov and the boundary point is probabilistically regular for the interior of the…

We provide a characterization of the set of real-valued functions that can be the value function of some polynomial game. Specifically, we prove that a function $u : \dR \to \dR$ is the value function of some polynomial game if and only if…

This paper studies the connections between mean-field games and the social welfare optimization problems. We consider a mean field game in functional spaces with a large population of agents, each of which seeks to minimize an individual…

In the present paper we investigate the problem of the existence of a value for differential games without Isaacs condition. For this we introduce a suitable concept of mixed strategies along a partition of the time interval, which are…

In this manuscript, we propose a structural condition on non-separable Hamiltonians, which we term displacement monotonicity condition, to study second order mean field games master equations. A rate of dissipation of a bilinear form is…

This paper studies the connection between a class of mean-field games and a social welfare optimization problem. We consider a mean-field game in function spaces with a large population of agents, and each agent seeks to minimize an…

In this paper, we study deterministic mean field games for agents who operate in a bounded domain. In this case, the existence and uniqueness of Nash equilibria cannot be deduced as for unrestricted state space because, for a large set of…

In this article, we study a simplified version of a density-dependent first-order mean field game, in which the players face a penalization equal to the population density at their final position. We consider the problem of finding an…

The desirable gambles framework provides a foundational approach to imprecise probability theory but relies heavily on linear utility assumptions. This paper introduces function-coherent gambles, a generalization that accommodates…

A mean field type differential game is a mathematical model of a large system of identical agents under mean-field interaction controlled by two players with opposite purposes. We study the case when the dynamics of each agent is given by…

Incentive mechanism is crucial for federated learning (FL) when rational clients do not have the same interests in the global model as the server. However, due to system heterogeneity and limited budget, it is generally impractical for the…