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Related papers: Quantum mean field games

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This paper establishes that $N$-player stochastic games with singular controls, either of bounded velocity or of finite variation, can both be approximated by mean field games (MFGs) with singular controls of bounded velocity. More…

Optimization and Control · Mathematics 2020-04-28 Haoyang Cao , Xin Guo , Joon Seok Lee

We define generalized quantum games by introducing the coherent payoff operators and propose a simple scheme to illustrate it. The scheme is implemented with a single spin qubit system and two entangled qubit system. The Nash Equilibrium…

Quantum Physics · Physics 2007-05-23 X. F. Liu , C. P. Sun

This paper establishes that a class of $N$-player stochastic games with singular controls, either of bounded velocity or of finite variation, can both be approximated by mean field games (MFGs) with singular controls of bounded velocity.…

Optimization and Control · Mathematics 2025-09-23 Haoyang Cao , Xin Guo , Joon Seok Lee

This paper proposes and studies a general form of dynamic $N$-player non-cooperative games called $\alpha$-potential games, where the change of a player's value function upon her unilateral deviation from her strategy is equal to the change…

Optimization and Control · Mathematics 2025-04-02 Xin Guo , Xinyu Li , Yufei Zhang

Non-cooperative and cooperative games with a very large number of players have many applications but remain generally intractable when the number of players increases. Introduced by Lasry and Lions, and Huang, Caines and Malham\'e, Mean…

In the flavour of categorical quantum mechanics, we extend nonlocal games to allow quantum questions and answers, using quantum sets (special symmetric dagger Frobenius algebras) and the quantum functions of Musto, Reutter, and Verdon…

Quantum Physics · Physics 2026-01-14 Adina Goldberg

Mean field type games (MFTGs) describe Nash equilibria between large coalitions: each coalition consists of a continuum of cooperative agents who maximize the average reward of their coalition while interacting non-cooperatively with a…

Computer Science and Game Theory · Computer Science 2025-07-29 Kai Shao , Jiacheng Shen , Mathieu Laurière

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

The goal of this paper is to study a Mean Field Game (MFG) system stemming from the harvesting of resources. Modelling the latter through a reaction-diffusion equation and the harvesters as competing rational agents, we are led to a…

Analysis of PDEs · Mathematics 2024-06-11 Ziad Kobeissi , Idriss Mazari-Fouquer , Domènec Ruiz-Balet

We present a many body approach for non-equilibrium behavior and self-generated glassiness in strongly correlated quantum systems. It combines the dynamical mean field theory of equilibrium systems with the replica theory for classical…

Disordered Systems and Neural Networks · Physics 2009-11-07 Harry Westfahl , Joerg Schmalian , Peter G Wolynes

Establishing the existence of Nash equilibria for partially observed stochastic dynamic games is known to be quite challenging, with the difficulties stemming from the noisy nature of the measurements available to individual players…

Systems and Control · Computer Science 2018-06-06 Naci Saldi , Tamer Basar , Maxim Raginsky

We present the first study of a dynamical quantum game. Each agent has a `memory' of her performance over the previous m timesteps, and her strategy can evolve in time. The game exhibits distinct regimes of optimality. For small m the…

Quantum Physics · Physics 2007-05-23 Roland Kay , Neil F. Johnson , Simon C. Benjamin

Over the last twenty years of research on quantum game theory have given us many ideas of how quantum games could be played. One of the most prominent ideas in the field is a model of quantum playing a 2x2 game introduced by J. Eisert, M.…

Quantum Physics · Physics 2021-05-26 Piotr Frąckiewicz

Nash equilibria are crucial for understanding game behavior and systems in economics, physics, biology, and computer science. A significant application arises from the connection between Nash equilibria and optimization problems . However,…

Quantum Physics · Physics 2025-11-14 Giovanni Ferrannini , Dario di Gregorio , Federico Fissore

Recently, the paper [12] introduces a derivative-free consensus-based particle method that finds the Nash equilibrium of non-convex multiplayer games, where it proves the global exponential convergence in the sense of mean-field law. This…

Optimization and Control · Mathematics 2025-05-21 Hui Huang , Jethro Warnett

In this paper, we study large population multi-agent reinforcement learning (RL) in the context of discrete-time linear-quadratic mean-field games (LQ-MFGs). Our setting differs from most existing work on RL for MFGs, in that we consider a…

Systems and Control · Electrical Eng. & Systems 2020-10-02 Muhammad Aneeq uz Zaman , Kaiqing Zhang , Erik Miehling , Tamer Başar

In recent years methods have been proposed to extend classical game theory into the quantum domain. This paper explores further extensions of these ideas that may have a substantial potential for further research. Upon reformulating quantum…

Quantum Physics · Physics 2007-05-23 F. M. C. Witte

We consider the problem of representing collective behavior of large populations and predicting the evolution of a population distribution over a discrete state space. A discrete time mean field game (MFG) is motivated as an interpretable…

Machine Learning · Computer Science 2018-04-24 Jiachen Yang , Xiaojing Ye , Rakshit Trivedi , Huan Xu , Hongyuan Zha

Mean-field games (MFG) were introduced to efficiently analyze approximate Nash equilibria in large population settings. In this work, we consider entropy-regularized mean-field games with a finite state-action space in a discrete time…

Computer Science and Game Theory · Computer Science 2022-07-26 Yue Guan , Mi Zhou , Ali Pakniyat , Panagiotis Tsiotras

This paper studies mean field game (MFG) of controls by featuring the joint distribution of the state and the control with the reflected state process along an exogenous stochastic reflection boundary. We contribute to the literature with a…

Optimization and Control · Mathematics 2025-11-10 Lijun Bo , Jingfei Wang , Xiang Yu