Related papers: A two-player zero-sum probabilistic game that appr…

We study new classes of games, called zero-sum equivalent games and zero-sum equivalent potential games, and prove decomposition theorems involving these classes of games. We say that two games are "strategically equivalent" if, for every…

This paper investigates mixed strategies in dynamic games with perfect information. We present an example to show that a player may obtain higher payoff by playing mixed strategy. By contrast, the main result of the paper shows that every…

We introduce a new non-zero-sum game of optimal stopping with asymmetric exercise opportunities. Given a stochastic process modelling the value of an asset, one player observes and can act on the process continuously, while the other player…

We consider a game, in which the dynamics is described by a non-linear Volterra integral equation of Hammerstein type with a weakly-singular kernel and the goals of the first and second players are, respectively, to minimize and maximize a…

We study a two-player, zero-sum, dynamic game with incomplete information where one of the players is more informed than his opponent. We analyze the limit value as the players play more and more frequently. The more informed player…

Bayesian regression games are a special class of two-player general-sum Bayesian games in which the learner is partially informed about the adversary's objective through a Bayesian prior. This formulation captures the uncertainty in regard…

In this paper, we present exploitability descent, a new algorithm to compute approximate equilibria in two-player zero-sum extensive-form games with imperfect information, by direct policy optimization against worst-case opponents. We prove…

We investigate an infinite dimensional partial differential equation of Isaacs' type, which arises from a zero-sum differential game between two masses. The evolution of the two masses is described by a controlled transport/continuity…

The paper is concerned with a zero-sum continuous-time stochastic differential game with a dynamics controlled by a Markov process and a terminal payoff. The value function of the original game is estimated using the value function of a…

Finding Nash equilibria in two-player zero-sum continuous games is a central problem in machine learning, e.g. for training both GANs and robust models. The existence of pure Nash equilibria requires strong conditions which are not…

Two-player quantitative zero-sum games provide a natural framework to synthesize controllers with performance guarantees for reactive systems within an uncontrollable environment. Classical settings include mean-payoff games, where the…

Two-player stochastic games are games with two 2 players and a randomised entity called "nature". A natural question to ask in this framework is the existence of strategies that ensure that an event happens with probability 1 (almost-sure…

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…

Using methods from the statistical mechanics of disordered systems we analyze the properties of bimatrix games with random payoffs in the limit where the number of pure strategies of each player tends to infinity. We analytically calculate…

We consider a convexity constrained Hamilton-Jacobi-Bellman-type obstacle problem for the value function of a zero-sum differential game with asymmetric information. We propose a convexity-preserving probabilistic numerical scheme for the…

We consider a zero-sum stochastic differential controller-and-stopper game in which the state process is a controlled diffusion evolving in a multi-dimensional Euclidean space. In this game, the controller affects both the drift and the…

We consider zero-sum stochastic games with perfect information and finitely many states and actions. The payoff is computed by a function which associates to each infinite sequence of states and actions a real number. We prove that if the…

In this paper, we extend the Descent framework, which enables learning and planning in the context of two-player games with perfect information, to the framework of stochastic games. We propose two ways of doing this, the first way…

In this paper we experiment with a 2-player strategy board game where playing models are evolved using reinforcement learning and neural networks. The models are evolved to speed up automatic game development based on human involvement at…

We consider two-player zero-sum stochastic games and propose a two-timescale $Q$-learning algorithm with function approximation that is payoff-based, convergent, rational, and symmetric between the two players. In two-timescale…