109 Hits in 6.3 sec

Learning in nonatomic games, Part I: Finite action spaces and population games [article]

Saeed Hadikhanloo and Rida Laraki and Panayotis Mertikopoulos and Sylvain Sorin
2021 arXiv   pre-print
We focus exclusively on games with finite action spaces; nonatomic games with continuous action spaces are treated in detail in Part II of this paper.  ...  We examine the long-run behavior of a wide range of dynamics for learning in nonatomic games, in both discrete and continuous time.  ...  Acknowledgments The authors acknowledge support by the COST Action CA16228 "European Network for Game Theory" (GAMENET), the FMJH Program PGMO under grant Damper, and the French National Research Agency  ... 
arXiv:2107.01595v1 fatcat:7hsiiepqwjgj3frzut3ieqtqai

Nonsmooth Aggregative Games with Coupling Constraints and Infinitely Many Classes of Players [article]

Paulin Jacquot, Cheng Wan
2018 arXiv   pre-print
nonatomic aggregative game, and the aggregative constraints in the finite-player games converge to the aggregative constraint of the nonatomic game, then a sequence of so-called variational Nash equilibria  ...  After defining a pure-action profile in a nonatomic aggregative game, where players have specific compact convex pure-action sets and nonsmooth convex cost functions, as a square-integrable function, we  ...  Acknowledgments We thank Sylvain Sorin, Stéphane Gaubert, Marco Mazzola, Olivier Beaude and Nadia Oudjane for their insightful comments.  ... 
arXiv:1806.06230v1 fatcat:x2wsx4vh5nbofaspxjbkg7mthq

Social Learning in Nonatomic Routing Games [article]

Emilien Macault, Marco Scarsini, Tristan Tomala
2021 arXiv   pre-print
We consider a discrete-time nonatomic routing game with variable demand and uncertain costs.  ...  We prove that these networks have a series-parallel structure and provide a counterexample to show that learning may fail in non-series-parallel networks.  ...  His research received partial support from the COST action GAMENET, the INdAM-GNAMPA Project 2020 "Random walks on random games," and the Italian MIUR PRIN 2017 Project ALGADIMAR "Algorithms, Games, and  ... 
arXiv:2009.11580v3 fatcat:ymr4ie7lnvbmpk4orw46dumxwi

Equilibria of nonatomic anonymous games [article]

Simone Cerreia-Vioglio, Fabio Maccheroni, David Schmeidler
2020 arXiv   pre-print
This notion encompasses and brings to nonatomic games recent concepts of equilibrium such as self-confirming, peer-confirming, and Berk–Nash. This augmented scope is our main motivation.  ...  In that paperthe existence of pure-strategy Nash equilibria has been proved for any nonatomic game with a continuum of players, endowed with an atomless countably additive probability.  ...  They were mostly developed for finite games and, inter alia, in this paper we extend them to nonatomic games.  ... 
arXiv:2005.01839v1 fatcat:lwcweftfgrbizpmhjm3axg6cai

Inducing Social Optimality in Games via Adaptive Incentive Design [article]

Chinmay Maheshwari and Kshitij Kulkarni and Manxi Wu and Shankar Sastry
2022 arXiv   pre-print
We propose a two-timescale learning dynamics to answer this question in both atomic and non-atomic games.  ...  and (iii) non-atomic network routing games.  ...  Each population iĨ is comprised of a continuum set of players with mass M i > 0. Individual players in each population can choose an action in a finite set S i .  ... 
arXiv:2204.05507v1 fatcat:t5hjudv5jrfvjdjyktejq67fjy

Evolutionary stability implies asymptotic stability under multiplicative weights [article]

Ioannis Avramopoulos
2016 arXiv   pre-print
computing evolutionarily stable states in nonlinear population games.  ...  nonatomic congestion games, which are well-known to be equipped with a convex potential function, and finding strict local maxima of quadratic programming problems, are special cases of the problem of  ...  Part of the work in this paper was performed during my stint as a senior researcher at Deutsche Telekom Laboratories (T-Labs) in Berlin, Germany between 2008 and 2011.  ... 
arXiv:1601.07267v2 fatcat:hv2q7rsxorfphgrivc2yzodtym

Multiplicative weights in monotropic games [article]

Ioannis Avramopoulos
2014 arXiv   pre-print
Monotropic games generalize strictly concave potential games and zero sum games with a unique minimax solution. Within the class of monotropic games, we study a multiplicative weights dynamic.  ...  We introduce a new class of population games that we call monotropic; these are games characterized by the presence of a unique globally neutrally stable Nash equilibrium.  ...  My interest in multiplicative weights grew out of a summer internship at Akamai Technologies in the summer of 2000 where I had the opportunity and privilege to work with Gary Miller and Joel Wein and interact  ... 
arXiv:1404.4163v2 fatcat:uxyjho36s5dkhdr4r3leg7fare

Mixed-Strategy Learning With Continuous Action Sets

Steven Perkins, Panayotis Mertikopoulos, David S. Leslie
2017 IEEE Transactions on Automatic Control  
in the case of potential games.  ...  We propose an actor-critic reinforcement learning algorithm that adapts mixed strategies over continuous action spaces.  ...  Smooth best responses also play an important part in discrete action games, particularly when learning is considered.  ... 
doi:10.1109/tac.2015.2511930 fatcat:dgqdzehar5hfxkek6qedo4q6pu

Coordinating users of shared facilities via data-driven predictive assistants and game theory [article]

Philipp Geiger, Michel Besserve, Justus Winkelmann, Claudius Proissl, Bernhard Schölkopf
2021 arXiv   pre-print
., "perfect" (probabilistic) predictions of what will happen, solve the coordination problem in the game-theoretic sense of selecting a Bayesian Nash equilibrium (BNE).  ...  Next we prove that such prophecies exist even in large-scale settings where only aggregated statistics about users are available. This entails a new (nonatomic) BNE existence result.  ...  The authors thank Carl-Johann Simon-Gabriel, Jonathan Williams and Sebastian Stark for insightful discussions and engineering support.  ... 
arXiv:1803.06247v6 fatcat:zkfocnamcfgkjabv5eqydo3u7i

Online Learning of Nash Equilibria in Congestion Games

Walid Krichene, Benjamin Drighès, Alexandre M. Bayen
2015 SIAM Journal of Control and Optimization  
In [19] , Kleinberg, Piliouras, and Tardos study the problem of online learning in atomic congestion games with finitely many players.  ...  This motivates the study of the game and the population dynamics in an online learning framework.  ...  We thank the anonymous reviewers and the editor for many insightful comments and suggestions.  ... 
doi:10.1137/140980685 fatcat:hyrprv6pvzal5a4emfyycyzcou

Learning Pure Nash Equilibrium in Smart Charging Games [article]

Benoît Sohet, Yezekael Hayel, Olivier Beaude, Alban Jeandin
2021 arXiv   pre-print
It is known that RLA converge towards the pure Nash Equilibria (NE) of finite congestion games and more generally, finite potential games.  ...  In this paper, finite congestion games with non-separable costs are shown to have an ordinal potential function, leading to the existence of an action-dependent continuous potential function.  ...  This type of potential is widely considered in population games [17] , as it serves as a Lyapunov function for strategies' dynamics, or in games with nonatomic players [18] .  ... 
arXiv:2111.06817v1 fatcat:27i545n5cjg6flkqmnj7kftlxa

Balancing Traffic in Networks: Redundancy, Learning and the Effect of Stochastic Fluctuations [article]

Panayotis Mertikopoulos, Aris L. Moustakas
2010 arXiv   pre-print
We study the distribution of traffic in networks whose users try to minimise their delays by adhering to a simple learning scheme inspired by the replicator dynamics of evolutionary game theory.  ...  In fact, if the network has no redundancy and the users are patient enough, we show that the long-term averages of the users' traffic flows converge to the vicinity of an equilibrium, and we also estimate  ...  Scarsini for a series of fruitful discussions on Braess's paradox which helped us clarify the differences between the equilibrial conditions that arise in congestion models.  ... 
arXiv:0912.4012v2 fatcat:iajxwnosz5fxxownsgciks4nnu

Generalization in Mean Field Games by Learning Master Policies [article]

Sarah Perrin and Mathieu Laurière and Julien Pérolat and Romuald Élie and Matthieu Geist and Olivier Pietquin
2021 arXiv   pre-print
Our approach relies on three ingredients: adding the current population distribution as part of the observation, approximating Master policies with neural networks, and training via Reinforcement Learning  ...  Mean Field Games (MFGs) can potentially scale multi-agent systems to extremely large populations of agents.  ...  Our approach is the first to tackle this question in the literature on MFGs. Background and Related Works We consider a finite state space X and finite action space A.  ... 
arXiv:2109.09717v1 fatcat:wwgozospdnbpblbyv6u5bo7zqu

Learning in anonymous nonatomic games with applications to first-order mean field games [article]

Saeed Hadikhanloo
2017 arXiv   pre-print
We introduce a model of anonymous games with the player dependent action sets.  ...  We propose several learning procedures based on the well-known Fictitious Play and Online Mirror Descent and prove their convergence to equilibrium under the classical monotonicity condition.  ...  I would very much like to thank Panayotis Mertikopoulos, Sylvain Sorin and my Phd directors Pierre Cardaliaguet and Rida Laraki, who provided insight and expertise that greatly assisted this research as  ... 
arXiv:1704.00378v1 fatcat:c54k34kknrhozdkecxp2skttce

Mean-Field-Type Games in Engineering [article]

Boualem Djehiche and Alain Tcheukam and Hamidou Tembine
2017 arXiv   pre-print
A mean-field-type game is a game in which the instantaneous payoffs and/or the state dynamics functions involve not only the state and the action profile but also the joint distributions of state-action  ...  networks, virus spread over networks, virtual machine resource management in cloud networks, synchronization of oscillators, energy-efficient buildings, online meeting and mobile crowdsensing.  ...  The authors would like to thank the Editor and the anonymous reviewers for interesting and constructive comments on the manuscript.  ... 
arXiv:1605.03281v3 fatcat:mq5doc4wc5cmteu4jrklnbve3q
« Previous Showing results 1 — 15 out of 109 results