Related papers: ZERO: Playing Mathematical Programming Games

Numerical simulations are ubiquitous in mathematics and computational science. Several industrial and clinical applications entail modeling complex multiphysics systems that evolve over a variety of spatial and temporal scales. This study…

Within the context of video games the notion of perfectly rational agents can be undesirable as it leads to uninteresting situations, where humans face tough adversarial decision makers. Current frameworks for stochastic games and…

Large language models (LLMs) have enabled rapid progress in automatic heuristic discovery (AHD), yet most existing methods are predominantly limited by static evaluation against fixed instance distributions, leading to potential overfitting…

Game theory finds nowadays a broad range of applications in engineering and machine learning. However, in a derivative-free, expensive black-box context, very few algorithmic solutions are available to find game equilibria. Here, we propose…

This paper investigates the discrete-time asynchronous games in which noncooperative agents seek to minimize their individual cost functions. Building on the assumption of partial asynchronism, i.e., each agent updates at least once within…

Cooperative games provide a framework to study cooperation among self-interested agents. They offer a number of solution concepts describing how the outcome of the cooperation should be shared among the players. Unfortunately, computational…

A binary constraint system game is a two-player one-round non-local game defined by a system of Boolean constraints. The game has a perfect quantum strategy if and only if the constraint system has a quantum satisfying assignment [R. Cleve…

This work studies an algorithm, which we call magnetic mirror descent, that is inspired by mirror descent and the non-Euclidean proximal gradient algorithm. Our contribution is demonstrating the virtues of magnetic mirror descent as both an…

Computing Nash equilibria of zero-sum games in classical and quantum settings is extensively studied. For general-sum games, computing Nash equilibria is PPAD-hard and the computing of a more general concept called correlated equilibria has…

We will describe a combinatorial game that models the problem of resolution of singularities of algebraic varieties over a field of characteristic zero. By giving a winning strategy for this game, we give another proof of the existence of…

Hex and Counter Wargames are adversarial two-player simulations of real military conflicts requiring complex strategic decision-making. Unlike classical board games, these games feature intricate terrain/unit interactions, unit stacking,…

We consider a two-player zero-sum game with integral payoff and with incomplete information on one side, where the payoff is chosen among a continuous set of possible payoffs. We prove that the value function of this game is solution of an…

Game theory is an established branch of mathematics that offers a rich set of mathematical tools for multi-person strategic decision making that can be used to model the interactions of decision makers in security problems who compete for…

Since DeepMind's AlphaZero, Zero learning quickly became the state-of-the-art method for many board games. It can be improved using a fully convolutional structure (no fully connected layer). Using such an architecture plus global pooling,…

By resorting to the vector space structure of finite games, skew-symmetric games (SSGs) are proposed and investigated as a natural subspace of finite games. First of all, for two player games, it is shown that the skew-symmetric games form…

We present efficient algorithms for computing optimal or approximately optimal strategies in a zero-sum game for which Player I has n pure strategies and Player II has an arbitrary number of pure strategies. We assume that for any given…

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…

Much of recent success in multiagent reinforcement learning has been in two-player zero-sum games. In these games, algorithms such as fictitious self-play and minimax tree search can converge to an approximate Nash equilibrium. While…

Two-player games such as board games have long been used as traditional benchmarks for reinforcement learning. This work revisits a policy optimization method with reverse Kullback-Leibler regularization and entropy regularization and…

We introduce DREAM, a deep reinforcement learning algorithm that finds optimal strategies in imperfect-information games with multiple agents. Formally, DREAM converges to a Nash Equilibrium in two-player zero-sum games and to an…