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We study discounted infinitely repeated games in which players agree on a cooperative mixed action profile but, at each step, observe only the realized pure actions. This form of imperfect monitoring breaks classical trigger strategies,…

Applications · Statistics 2026-03-09 Aymeric Capitaine , Antoine Scheid , Etienne Boursier , Alain Durmus , Michael I. Jordan

This paper considers discounted infinite horizon mean field games by extending the probabilistic weak formulation of the game as introduced by Carmona and Lacker (2015). Under similar assumptions as in the finite horizon game, we prove…

Optimization and Control · Mathematics 2024-07-08 René Carmona , Ludovic Tangpi , Kaiwen Zhang

Mean-field games have been studied under the assumption of very large number of players. For such large systems, the basic idea consists to approximate large games by a stylized game model with a continuum of players. The approach has been…

Computer Science and Game Theory · Computer Science 2014-04-08 Hamidou Tembine

In this work, we study the convergence rate of the $N$-player LQG game with a Markov chain common noise towards its asymptotic Mean Field Game. By postulating a Markovian structure via two auxiliary processes for the first and second…

Optimization and Control · Mathematics 2023-08-30 Jiamin Jian , Peiyao Lai , Qingshuo Song , Jiaxuan Ye

We consider a general class of finite-player stochastic games with mean-field interaction, in which the linear-quadratic cost functional includes linear operators acting on controls in $L^2$. We propose a novel approach for deriving the…

Optimization and Control · Mathematics 2024-02-16 Eduardo Abi Jaber , Eyal Neuman , Moritz Voß

In this paper, we investigate a partially observable zero sum games where the state process is a discrete time Markov chain. We consider a general utility function in the optimization criterion. We show the existence of value for both…

Optimization and Control · Mathematics 2022-11-16 Arnab Bhabak , Subhamay saha

Mean field games are limit models for symmetric $N$-player games with interaction of mean field type as $N\to\infty$. The limit relation is often understood in the sense that a solution of a mean field game allows to construct approximate…

Probability · Mathematics 2017-05-29 Markus Fischer

Financial markets and more generally macro-economic models involve a large number of individuals interacting through variables such as prices resulting from the aggregate behavior of all the agents. Mean field games have been introduced to…

Optimization and Control · Mathematics 2021-07-12 René Carmona , Mathieu Laurière

We study the problem of computing an approximate Nash equilibrium of a game whose strategy space is continuous without access to gradients of the utility function. Such games arise, for example, when players' strategies are represented by…

Computer Science and Game Theory · Computer Science 2025-10-28 Carlos Martin , Tuomas Sandholm

The paper shows that smooth fictitious play converges to a neighborhood of a pure-strategy Nash equilibrium with probability 1 in almost all $N\times 2$ ($N$-player, two-action) potential games. The neighborhood of convergence may be made…

Computer Science and Game Theory · Computer Science 2019-12-03 Brian Swenson , H. Vincent Poor

We present a framework for computing approximate mixed-strategy Nash equilibria of continuous-action games. It is a modification of the traditional double oracle algorithm, extended to multiple players and continuous action spaces. Unlike…

Computer Science and Game Theory · Computer Science 2024-06-14 Carlos Martin , Tuomas Sandholm

This paper investigates a class of general linear-quadratic mean field games with common noise, where the diffusion terms of the system contain the state variables, control variables, and the average state terms. We solve the problem using…

Optimization and Control · Mathematics 2025-08-29 Yu Si , Jingtao Shi

Mean-field games with absorption is a class of games, that have been introduced in Campi and Fischer (2018) and that can be viewed as natural limits of symmetric stochastic differential games with a large number of players who, interacting…

Probability · Mathematics 2021-11-05 Luciano Campi , Maddalena Ghio , Giulia Livieri

Distributed Nash equilibrium seeking of aggregative games is investigated and a continuous-time algorithm is proposed. The algorithm is designed by virtue of projected gradient play dynamics and distributed average tracking dynamics, and is…

Optimization and Control · Mathematics 2021-12-07 Shu Liang , Peng Yi , Yiguang Hong , Kaixiang Peng

We study two-player security games which can be viewed as sequences of nonzero-sum matrix games played by an Attacker and a Defender. The evolution of the game is based on a stochastic fictitious play process, where players do not have…

Computer Science and Game Theory · Computer Science 2016-11-17 Kien C. Nguyen , Tansu Alpcan , Tamer Başar

This paper proposes and studies a class of discrete-time finite-time-horizon Stackelberg mean-field games, with one leader and an infinite number of identical and indistinguishable followers. In this game, the objective of the leader is to…

Optimization and Control · Mathematics 2022-10-11 Xin Guo , Anran Hu , Jiacheng Zhang

As the earliest and one of the most fundamental learning dynamics for computing NE, fictitious play (FP) has being receiving incessant research attention and finding games where FP would converge (games with FPP) is one central question in…

Optimization and Control · Mathematics 2024-12-31 Zhouming Wu , Yifen Mu , Xiaoguang Yang

A classic model to study strategic decision making in multi-agent systems is the normal-form game. This model can be generalised to allow for an infinite number of pure strategies leading to continuous games. Multi-objective normal-form…

Computer Science and Game Theory · Computer Science 2023-03-02 Willem Röpke , Carla Groenland , Roxana Rădulescu , Ann Nowé , Diederik M. Roijers

In the presence of a common noise, we study the convergence problems in mean field game (MFG) and mean field control (MFC) problem where the cost function and the state dynamics depend upon the joint conditional distribution of the…

Probability · Mathematics 2023-08-29 Mao Fabrice Djete

In this paper, we consider a class of linear quadratic extended mean field games (MFGs) with common noises where the state coefficients and the cost functional vary with the mean field term in a nonlinear way. Based on stochastic maximum…

Optimization and Control · Mathematics 2023-11-08 Tianjiao Hua , Peng Luo