Related papers: Convergence of Heterogeneous Learning Dynamics in …

We provide a complete characterization for uniqueness of equilibria in unconstrained polymatrix games. We show that while uniqueness is natural for coordination and general polymatrix games, zero-sum games require that the dimension of the…

This paper examines multiplayer symmetric constant-sum games with more than two players in a competitive setting, including examples like Mahjong, Poker, and various board and video games. In contrast to two-player zero-sum games,…

Games, in their mathematical sense, are everywhere (game industries, economics, defense, education, chemistry, biology, ...).Search algorithms in games are artificial intelligence methods for playing such games. Unfortunately, there is no…

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…

We study zero-sum games in the space of probability distributions over the Euclidean space $\mathbb{R}^d$ with entropy regularization, in the setting when the interaction function between the players is smooth and strongly convex-strongly…

We consider a class of fully stochastic and fully distributed algorithms, that we prove to learn equilibria in games. Indeed, we consider a family of stochastic distributed dynamics that we prove to converge weakly (in the sense of weak…

Successful algorithms have been developed for computing Nash equilibrium in a variety of finite game classes. However, solving continuous games -- in which the pure strategy space is (potentially uncountably) infinite -- is far more…

We consider control of heterogeneous players repeatedly playing an anti-coordination network game. In an anti-coordination game, each player has an incentive to differentiate its action from its neighbors. At each round of play, players…

Two player zero sum simultaneous action games are common in video games, financial markets, war, business competition, and many other settings. We first introduce the fundamental concepts of reinforcement learning in two player zero sum…

We develop provably efficient reinforcement learning algorithms for two-player zero-sum finite-horizon Markov games with simultaneous moves. To incorporate function approximation, we consider a family of Markov games where the reward…

Generating payoff matrices of normal-form games at random, we calculate the frequency of games with a unique pure strategy Nash equilibrium in the ensemble of $n$-player, $m$-strategy games. These are perfectly predictable as they must…

We present a systematic investigation of the quantum games, constructed using a novel repeated game protocol, when played repeatedly ad infinitum. We focus on establishing that such repeated games -- by virtue of inherent quantum-mechanical…

This paper considers repeated games in which one player has more information about the game than the other players. In particular, we investigate repeated two-player zero-sum games where only the column player knows the payoff matrix A of…

Correlations and other collective phenomena in a schematic model of heterogeneous binary agents (individual spin-glass samples) are considered on the complete graph and also on 2d and 3d regular lattices. The system's stochastic dynamics is…

We formulate and study a general time-varying multi-agent system where players repeatedly compete under incomplete information. Our work is motivated by scenarios commonly observed in online advertising and retail marketplaces, where agents…

We consider multi-agent decision making where each agent's cost function depends on all agents' strategies. We propose a distributed algorithm to learn a Nash equilibrium, whereby each agent uses only obtained values of her cost function at…

In this paper, we formulate a two-player zero-sum game under dynamic constraints defined by hybrid dynamical equations. The game consists of a min-max problem involving a cost functional that depends on the actions and resulting solutions…

Learning from repeated play in a fixed two-player zero-sum game is a classic problem in game theory and online learning. We consider a variant of this problem where the game payoff matrix changes over time, possibly in an adversarial…

We show that natural classes of regularized learning algorithms with a form of recency bias achieve faster convergence rates to approximate efficiency and to coarse correlated equilibria in multiplayer normal form games. When each player in…

Self-serving, rational agents sometimes cooperate to their mutual benefit. The two-player iterated prisoner's dilemma game is a model for including the emergence of cooperation. It is generally believed that there is no simple ultimatum…