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We here address the question of restoration of uniqueness in mean-field games deriving from deterministic differential games with a large number of players. The general strategy for restoring uniqueness is inspired from earlier similar…

Probability · Mathematics 2018-04-11 Francois Delarue

This paper introduces a framework of Constrained Mean-Field Games (CMFGs), where each agent solves a constrained Markov decision process (CMDP). This formulation captures scenarios in which agents' strategies are subject to feasibility,…

Optimization and Control · Mathematics 2025-10-15 Anran Hu , Zijiu Lyu

We consider multi-agent decision making where each agent optimizes its convex cost function subject to individual and coupling constraints. The constraint sets are compact convex subsets of a Euclidean space. To learn Nash equilibria, we…

Optimization and Control · Mathematics 2018-10-16 Tatiana Tatarenko , Maryam Kamgarpour

In this paper, we consider a large class of constrained non-cooperative stochastic Markov games with countable state spaces and discounted cost criteria. In one-player case, i.e., constrained discounted Markov decision models, it is…

Optimization and Control · Mathematics 2021-12-16 Anna Jaśkiewicz , Andrzej S. Nowak

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…

Optimization and Control · Mathematics 2018-02-15 Sen Li , Wei Zhang , Lin Zhao

We consider seeking a Nash equilibrium (NE) of a monotone game, played by dynamic agents which are modeled as a class of lower-triangular nonlinear uncertain dynamics with external disturbances. We establish a general framework that…

Optimization and Control · Mathematics 2025-11-04 Weijian Li , Yutao Tang

We introduce a new mean field kinetic model for systems of rational agents interacting in a game theoretical framework. This model is inspired from non-cooperative anonymous games with a continuum of players and Mean-Field Games. The large…

Mathematical Physics · Physics 2012-12-27 Pierre Degond , Jian-Guo Liu , Christian Ringhofer

In this paper, we study a class of linear-quadratic (LQ) mean field games of controls with common noises and their corresponding $N$-player games. The theory of mean field game of controls considers a class of mean field games where the…

Optimization and Control · Mathematics 2022-06-13 Min Li , Chenchen Mou , Zhen Wu , Chao Zhou

This paper continues the study of the mean field game (MFG) convergence problem: In what sense do the Nash equilibria of $n$-player stochastic differential games converge to the mean field game as $n\rightarrow\infty$? Previous work on this…

Probability · Mathematics 2018-08-09 Daniel Lacker

We study a sequence of symmetric $n$-player stochastic differential games driven by both idiosyncratic and common sources of noise, in which players interact with each other through their empirical distribution. The unique Nash equilibrium…

Probability · Mathematics 2018-04-24 Francois Delarue , Daniel Lacker , Kavita Ramanan

Nash equilibrium is one of the most influential solution concepts in game theory. With the development of computer science and artificial intelligence, there is an increasing demand on Nash equilibrium computation, especially for Internet…

Computer Science and Game Theory · Computer Science 2023-12-19 Hanyu Li , Wenhan Huang , Zhijian Duan , David Henry Mguni , Kun Shao , Jun Wang , Xiaotie Deng

An axiomatic characterization of Nash equilibrium is provided for games in normal form. The Nash equilibrium correspondence is shown to be fully characterized by four simple and intuitive axioms, two of which are inspired by contraction and…

Theoretical Economics · Economics 2025-12-04 Michele Crescenzi

We consider a symmetric $n$-player nonzero-sum stochastic differential game with controlled jumps and mean-field type interaction among the players. Each player minimizes some expected cost by affecting the drift as well as the jump part of…

Probability · Mathematics 2018-05-14 Chiara Benazzoli , Luciano Campi , Luca Di Persio

We study mean field portfolio games with consumption. For general market parameters, we establish a one-to-one correspondence between Nash equilibria of the game and solutions to some FBSDE, which is proved to be equivalent to some BSDE.…

Mathematical Finance · Quantitative Finance 2022-12-08 Guanxing Fu

Several notions of game enjoy a Nash-like notion of equilibrium without guarantee of existence. There are different ways of weakening a definition of Nash-like equilibrium in order to guarantee the existence of a weakened equilibrium.…

Computer Science and Game Theory · Computer Science 2007-12-11 Stéphane Le Roux

We consider a nonzero-sum N-player Markov game on an abstract measurable state space with compact metric action spaces. The payoff functions are bounded Carath\'eodory functions and the transitions of the system are assumed to have a…

Optimization and Control · Mathematics 2023-05-09 François Dufour , Tomás Prieto-Rumeau

We analyse the computational complexity of finding Nash equilibria in turn-based stochastic multiplayer games with omega-regular objectives. We show that restricting the search space to equilibria whose payoffs fall into a certain interval…

Computer Science and Game Theory · Computer Science 2015-07-01 Michael Ummels , Dominik Wojtczak

We construct Nash-equilibria in mean-field portfolio games of optimal investment and hedging under relative performance concerns with exponential (CARA) utility preferences. Common noise dynamics are modeled by integer-valued random…

Optimization and Control · Mathematics 2026-01-08 Dirk Becherer , Stefanie Hesse

In this paper, we investigate the mean field games with $K$ classes of agents who are weakly coupled via the empirical measure. The underlying dynamics of the representative agents is assumed to be a controlled nonlinear Markov process…

Probability · Mathematics 2012-04-09 Vassili N. Kolokoltsov , Jiajie Li , Wei Yang

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…

Optimization and Control · Mathematics 2021-01-05 Minyi Huang , Yan Ma