Related papers: Exponentially fast convergence to (strict) equilib…

We study the quality of outcomes in repeated games when the population of players is dynamically changing and participants use learning algorithms to adapt to the changing environment. Game theory classically considers Nash equilibria of…

This paper considers a time-varying game with $N$ players. Every time slot, players observe their own random events and then take a control action. The events and control actions affect the individual utilities earned by each player. The…

Follow the regularized leader FTRL is the premier algorithm for online optimization. However, despite decades of research on its convergence in constrained optimization -- and potential games in particular -- its behavior remained hitherto…

We study online optimization methods for zero-sum games, a fundamental problem in adversarial learning in machine learning, economics, and many other domains. Traditional methods approximate Nash equilibria (NE) using either regret-based…

While Nash equilibrium has emerged as the central game-theoretic solution concept, many important games contain several Nash equilibria and we must determine how to select between them in order to create real strategic agents. Several Nash…

When two players are engaged in a repeated game with unknown payoff matrices, they may use single-agent multi-armed bandit algorithms to choose the actions independent of each other. We show that when the players use Thompson sampling, the…

We argue that the existing regret matchings for Nash equilibrium approximation conduct "jumpy" strategy updating when the probabilities of future plays are set to be proportional to positive regret measures. We propose a geometrical regret…

We study the convergence of Optimistic Gradient Descent Ascent in unconstrained bilinear games. In a first part, we consider the zero-sum case and extend previous results by Daskalakis et al. in 2018, Liang and Stokes in 2019, and others:…

Prediction is a well-studied machine learning task, and prediction algorithms are core ingredients in online products and services. Despite their centrality in the competition between online companies who offer prediction-based products,…

This paper examines the convergence of no-regret learning in Cournot games with continuous actions. Cournot games are the essential model for many socio-economic systems, where players compete by strategically setting their output quantity.…

Data-driven modeling increasingly requires to find a Nash equilibrium in multi-player games, e.g. when training GANs. In this paper, we analyse a new extra-gradient method for Nash equilibrium finding, that performs gradient extrapolations…

We prove that in a normal form n-player game with m actions for each player, there exists an approximate Nash equilibrium where each player randomizes uniformly among a set of O(log(m) + log(n)) pure strategies. This result induces an…

In this paper, we investigate a distributed learning scheme for a broad class of stochastic optimization problems and games that arise in signal processing and wireless communications. The proposed algorithm relies on the method of matrix…

Understanding the convergence landscape of multi-agent learning is a fundamental problem of great practical relevance in many applications of artificial intelligence and machine learning. While it is known that learning dynamics converge to…

Nash equilibria provide a principled framework for modeling interactions in multi-agent decision-making and control. However, many equilibrium-seeking methods implicitly assume that each agent has access to the other agents' objectives and…

We analyze the performance of the best-response dynamic across all normal-form games using a random games approach. The playing sequence -- the order in which players update their actions -- is essentially irrelevant in determining whether…

Bargaining games, where agents attempt to agree on how to split utility, are an important class of games used to study economic behavior, which motivates a study of online learning algorithms in these games. In this work, we tackle when…

This paper introduces an equilibrium framework based on sequential sampling in which players face strategic uncertainty over their opponents' behavior and acquire informative signals to resolve it. Sequential sampling equilibrium delivers a…

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…

We consider a dynamical approach to game in extensive forms. By restricting the convertibility relation over strategy profiles, we obtain a semi-potential (in the sense of Kukushkin), and we show that in finite games the corresponding…