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Related papers: Value Iteration Algorithm for Mean-field Games

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This paper studies the existence and approximation of equilibria for general time-inconsistent mean field game (MFG) problems in continuous time. To handle the intricate nonlocal equilibrium Hamilton-Jacobi-Bellman (EHJB) system arising…

Optimization and Control · Mathematics 2026-05-29 Erhan Bayraktar , Zhenhua Wang , Xiang Yu , Keyu Zhang

We describe an efficient algorithm to compute solutions for the general two-player Blotto game on n battlefields with heterogeneous values. While explicit constructions for such solutions have been limited to specific, largely symmetric or…

Computer Science and Game Theory · Computer Science 2022-06-01 Vianney Perchet , Philippe Rigollet , Thibaut Le Gouic

Value iteration is a well-known method of solving Markov Decision Processes (MDPs) that is simple to implement and boasts strong theoretical convergence guarantees. However, the computational cost of value iteration quickly becomes…

Machine Learning · Computer Science 2021-07-26 Guanting Chen , Johann Demetrio Gaebler , Matt Peng , Chunlin Sun , Yinyu Ye

We study a multi-agent decision problem in population games, where agents select from multiple available strategies and continually revise their selections based on the payoffs associated with these strategies. Unlike conventional…

Multiagent Systems · Computer Science 2024-09-17 Shinkyu Park

Reinforcement learning has been successful both empirically and theoretically in single-agent settings, but extending these results to multi-agent reinforcement learning in general-sum Markov games remains challenging. This paper studies…

Machine Learning · Computer Science 2026-04-07 Narim Jeong , Donghwan Lee

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…

Optimization and Control · Mathematics 2024-09-13 Erhan Bayraktar , Zhenhua Wang

The standard solution concept for stochastic games is Markov perfect equilibrium (MPE); however, its computation becomes intractable as the number of players increases. Instead, we consider mean field equilibrium (MFE) that has been…

Theoretical Economics · Economics 2020-06-05 Bar Light , Gabriel Weintraub

We study algorithms for solving parity, mean-payoff and energy games. We propose a systematic framework, which we call Fast value iteration, for describing, comparing, and proving correctness of such algorithms. The approach is based on…

Computer Science and Game Theory · Computer Science 2025-02-13 Michaël Cadilhac , Antonio Casares , Pierre Ohlmann

In this paper, we consider mean-field games where the interaction of each player with the mean-field takes into account not only the states of the players but also their collective behavior, To do so, we develop a random variable framework…

Analysis of PDEs · Mathematics 2015-06-23 Diogo A. Gomes , Vardan K. Voskanyan

We are interested in the study of stochastic games for which each player faces an optimal stopping problem. In our setting, the players may interact through the criterion to optimise as well as through their dynamics. After briefly…

Probability · Mathematics 2025-09-03 Dylan Possamaï , Mehdi Talbi

We propose a discrete time graphon game formulation on continuous state and action spaces using a representative player to study stochastic games with heterogeneous interaction among agents. This formulation admits both philosophical and…

Optimization and Control · Mathematics 2024-06-07 Fuzhong Zhou , Chenyu Zhang , Xu Chen , Xuan Di

Multi-agent reinforcement learning methods have shown remarkable potential in solving complex multi-agent problems but mostly lack theoretical guarantees. Recently, mean field control and mean field games have been established as a…

Machine Learning · Computer Science 2021-12-20 Kai Cui , Anam Tahir , Mark Sinzger , Heinz Koeppl

Stochastic games provide a framework for interactions among multiple agents and enable a myriad of applications. In these games, agents decide on actions simultaneously, the state of every agent moves to the next state, and each agent…

Machine Learning · Computer Science 2019-10-10 Mridul Agarwal , Vaneet Aggarwal , Arnob Ghosh , Nilay Tiwari

For two-person dynamic zero-sum games (both discrete and continuous settings), we investigate the limit of value functions of finite horizon games with long run average cost as the time horizon tends to infinity and the limit of value…

Optimization and Control · Mathematics 2017-09-26 Dmitry Khlopin

In this paper we study a mean field model for discrete time, finite number of states, dynamic games. These models arise in situations that involve a very large number of agents moving from state to state according to certain optimality…

Optimization and Control · Mathematics 2009-03-10 Diogo A. Gomes , Joana Mohr , Rafael R. Souza

The purpose of this paper is to provide a complete probabilistic analysis of a large class of stochastic differential games for which the interaction between the players is of mean-field type. We implement the Mean-Field Games strategy…

Probability · Mathematics 2012-10-23 Rene Carmona , Francois Delarue

The price of anarchy, originally introduced to quantify the inefficiency of selfish behavior in routing games, is extended to mean field games. The price of anarchy is defined as the ratio of a worst case social cost computed for a mean…

Optimization and Control · Mathematics 2018-08-31 Rene Carmona , Christy V. Graves , Zongjun Tan

We compute equilibrium strategies in multi-stage games with continuous signal and action spaces as they are widely used in the management sciences and economics. Examples include sequential sales via auctions, multi-stage elimination…

Computer Science and Game Theory · Computer Science 2024-07-23 Fabian R. Pieroth , Nils Kohring , Martin Bichler

In this paper, we consider a finite horizon, non-stationary, mean field games (MFG) with a large population of homogeneous players, sequentially making strategic decisions, where each player is affected by other players through an aggregate…

Systems and Control · Electrical Eng. & Systems 2020-04-07 Rajesh K Mishra , Deepanshu Vasal , Sriram Vishwanath

In this work, we investigate a security game between an attacker and a defender, originally proposed in \cite{emadi2019security}. As is well known, the combinatorial nature of security games leads to a large cost matrix. Therefore,…

Computer Science and Game Theory · Computer Science 2020-07-30 HAmid Emadi , Sourabh Bhattacharya