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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…
Wide machine learning tasks can be formulated as non-convex multi-player games, where Nash equilibrium (NE) is an acceptable solution to all players, since no one can benefit from changing its strategy unilaterally. Attributed to the…
We present a simple game model where agents with different memory lengths compete for finite resources. We show by simulation and analytically that an instability exists at a critical memory length, and as a result, different memory lengths…
In this paper we consider the problem of finding a Nash equilibrium (NE) via zeroth-order feedback information in games with merely monotone pseudogradient mapping. Based on hybrid system theory, we propose a novel extremum seeking…
We study equilibrium concepts in non-cooperative games under uncertainty where both beliefs and mixed strategies are represented by non-additive measures (capacities). In contrast to the classical Nash framework based on additive…
We present a new model of incomplete information games without private information in which the players use a distributionally robust optimization approach to cope with the payoff uncertainty. With some specific restrictions, we show that…
We study the existence of approximate pure Nash equilibria ($\alpha$-PNE) in weighted atomic congestion games with polynomial cost functions of maximum degree $d$. Previously it was known that $d$-approximate equilibria always exist, while…
Self-play is a technique for machine learning in multi-agent systems where a learning algorithm learns by interacting with copies of itself. Self-play is useful for generating large quantities of data for learning, but has the drawback that…
A Nash equilibrium has become important solution concept for analyzing the decision making in Game theory. In this paper, we consider the problem of computing Nash equilibria of a subclass of generic finite normal form games. We define…
Several notions of game enjoy a Nash-like notion of equilibrium without guarantee of existence. There are different ways of weakening a definition of Nash-like equilibrium in order to guarantee the existence of a weakened equilibrium.…
This work considers a stochastic Nash game in which each player solves a parameterized stochastic optimization problem. In deterministic regimes, best-response schemes have been shown to be convergent under a suitable spectral property…
Combinatorial games lead to several interesting, clean problems in algorithms and complexity theory, many of which remain open. The purpose of this paper is to provide an overview of the area to encourage further research. In particular, we…
Reinforcement Learning Algorithms (RLA) are useful machine learning tools to understand how decision makers react to signals. It is known that RLA converge towards the pure Nash Equilibria (NE) of finite congestion games and more generally,…
Network congestion games are a convenient model for reasoning about routing problems in a network: agents have to move from a source to a target vertex while avoiding congestion, measured as a cost depending on the number of players using…
We provide a complete characterization for the computational complexity of finding approximate equilibria in two-action graphical games. We consider the two most well-studied approximation notions: $\varepsilon$-Nash equilibria…
Finite-horizon probabilistic multiagent concurrent game systems, also known as finite multiplayer stochastic games, are a well-studied model in computer science due to their ability to represent a wide range of real-world scenarios…
We study reinforcement learning for two-player zero-sum Markov games with simultaneous moves in the finite-horizon setting, where the transition kernel of the underlying Markov games can be parameterized by a linear function over the…
Regret-based algorithms are highly efficient at finding approximate Nash equilibria in sequential games such as poker games. However, most regret-based algorithms, including counterfactual regret minimization (CFR) and its variants, rely on…
This paper studies the complexity of solving two classes of non-cooperative games in a distributed manner in which the players communicate with a set of system nodes over noisy communication channels. The complexity of solving each game…
Game theory provides a well-established framework for the analysis of concurrent and multi-agent systems. The basic idea is that concurrent processes (agents) can be understood as corresponding to players in a game; plays represent the…