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We investigate convergence of decentralized fictitious play (DFP) in near-potential games, wherein agents preferences can almost be captured by a potential function. In DFP agents keep local estimates of other agents' empirical frequencies,…

Computer Science and Game Theory · Computer Science 2022-01-31 Sarper Aydin , Sina Arefizadeh , Ceyhun Eksin

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

Fictitious play (FP) is a canonical game-theoretic learning algorithm which has been deployed extensively in decentralized control scenarios. However standard treatments of FP, and of many other game-theoretic models, assume rather…

Optimization and Control · Mathematics 2016-09-29 Brian Swenson , Soummya Kar , João Xavier , David S. Leslie

The paper is concerned with distributed learning in large-scale games. The well-known fictitious play (FP) algorithm is addressed, which, despite theoretical convergence results, might be impractical to implement in large-scale settings due…

Optimization and Control · Mathematics 2016-11-17 Brian Swenson , Soummya Kar , Joao Xavier

The paper studies the highly prototypical Fictitious Play (FP) algorithm, as well as a broad class of learning processes based on best-response dynamics, that we refer to as FP-type algorithms. A well-known shortcoming of FP is that, while…

Optimization and Control · Mathematics 2015-04-21 Brian Swenson , Soummya Kar , Joao Xavier

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

Certain but important classes of strategic-form games, including zero-sum and identical-interest games, have the fictitious-play-property (FPP), i.e., beliefs formed in fictitious play dynamics always converge to a Nash equilibrium (NE) in…

Computer Science and Game Theory · Computer Science 2022-05-24 Muhammed O. Sayin , Kaiqing Zhang , Asuman Ozdaglar

We study the convergence properties of decentralized fictitious play (DFP) for the class of near-potential games where the incentives of agents are nearly aligned with a potential function. In DFP, agents share information only with their…

Optimization and Control · Mathematics 2021-03-19 Sarper Aydın , Sina Arefizadeh , Ceyhun Eksin

In 1964 Shapley devised a family of games for which fictitious play fails to converge to Nash equilibrium. The games are two-player non-zero-sum with 3 pure strategies per player. Shapley assumed that each player played a specific pure…

Computer Science and Game Theory · Computer Science 2023-12-21 Sam Ganzfried

We develop the fictitious play algorithm in the context of the linear programming approach for mean field games of optimal stopping and mean field games with regular control and absorption. This algorithm allows to approximate the mean…

Optimization and Control · Mathematics 2023-01-25 Roxana Dumitrescu , Marcos Leutscher , Peter Tankov

A mean-field game (MFG) seeks the Nash Equilibrium of a game involving a continuum of players, where the Nash Equilibrium corresponds to a fixed point of the best-response mapping. However, simple fixed-point iterations do not always…

Optimization and Control · Mathematics 2025-07-15 Jiajia Yu , Xiuyuan Cheng , Jian-Guo Liu , Hongkai Zhao

We introduce a novel class of Nash equilibrium seeking dynamics for non-cooperative games with a finite number of players, where the convergence to the Nash equilibrium is bounded by a KL function with a settling time that can be upper…

Optimization and Control · Mathematics 2020-12-25 Jorge I. Poveda , Miroslav Krstic , Tamer Basar

Considering the interaction through mutual interference of the different radio devices, the channel selection (CS) problem in decentralized parallel multiple access channels can be modeled by strategic-form games. Here, we show that the CS…

Computer Science and Game Theory · Computer Science 2010-09-28 S. M. Perlaza , H. Tembine , S. Lasaulce , V. Quintero-Florez

Fictitious play is a simple and widely studied adaptive heuristic for playing repeated games. It is well known that fictitious play fails to be Hannan consistent. Several variants of fictitious play including regret matching, generalized…

Computer Science and Game Theory · Computer Science 2017-04-12 Zifan Li , Ambuj Tewari

We study two-layer neural networks in the mean field limit, where the number of neurons tends to infinity. In this regime, the optimization over the neuron parameters becomes the optimization over the probability measures, and by adding an…

Optimization and Control · Mathematics 2023-08-17 Fan Chen , Zhenjie Ren , Songbo Wang

We study the long-term behavior of the fictitious play process in repeated extensive-form games of imperfect information with perfect recall. Each player maintains incorrect beliefs that the moves at all information sets, except the one at…

Computer Science and Game Theory · Computer Science 2025-04-28 Jason Castiglione , Gürdal Arslan

In this paper, we deepen the analysis of continuous time Fictitious Play learning algorithm to the consideration of various finite state Mean Field Game settings (finite horizon, $\gamma$-discounted), allowing in particular for the…

Optimization and Control · Mathematics 2020-10-27 Sarah Perrin , Julien Perolat , Mathieu Laurière , Matthieu Geist , Romuald Elie , Olivier Pietquin

Decentralised optimisation tasks are important components of multi-agent systems. These tasks can be interpreted as n-player potential games: therefore game-theoretic learning algorithms can be used to solve decentralised optimisation…

Multiagent Systems · Computer Science 2013-01-16 Michalis Smyrnakis

This paper considers mean field games with optimal stopping time (OSMFGs) where agents make optimal exit decisions, the coupled obstacle and Fokker-Planck equations in such models pose challenges versus classic MFGs. This paper proposes a…

Numerical Analysis · Mathematics 2023-10-10 Chengfeng Shen , Yifan Luo , Zhennan Zhou

In this paper, we apply the idea of fictitious play to design deep neural networks (DNNs), and develop deep learning theory and algorithms for computing the Nash equilibrium of asymmetric $N$-player non-zero-sum stochastic differential…

Optimization and Control · Mathematics 2020-09-07 Ruimeng Hu