arXiv research

Study best-response learning dynamics in zero-sum polymatrix games under full and minimal information settings.

Just as war is sometimes fallaciously represented as a zero sum game -- when in fact war is a negative sum game - stock market trading, a positive sum game over time, is often erroneously represented as a zero sum game. This is called the "zero sum fallacy" -- the erroneous belief that one trader in a stock market exch…

Gradient methods converge exponentially in concave network games.

Gradient Descent Ascent converges to von-Neumann solution in hidden zero-sum games.

Study Nash equilibrium in non-zero-sum game with Bermudan strategies.

New algorithm finds near-optimal policies efficiently in zero-sum games.

Paper studies competitive networks where teams aim to minimize their own objectives, adapting to each other's strategies.

New assumptions and algorithm solve offline two-player zero-sum Markov games.

New game approximates mean curvature flow evolution.

Study proposes new OPE estimators for two-player zero-sum games.

We study the global convergence of policy optimization for finding the Nash equilibria (NE) in zero-sum linear quadratic (LQ) games. To this end, we first investigate the landscape of LQ games, viewing it as a nonconvex-nonconcave saddle-point problem in the policy space. Specifically, we show that despite its nonconve…

We consider the problem of two-player zero-sum games. This problem is formulated as a min-max Markov game in the literature. The solution of this game, which is the min-max payoff, starting from a given state is called the min-max value of the state. In this work, we compute the solution of the two-player zero-sum game…

This work finds mixed equilibria in zero-sum games using interacting particle dynamics.

Algorithm learns from changing zero-sum games with no regret.

Paper proposes a mean-field gradient descent for zero-sum games, proving convergence to Nash equilibrium.

Study on convergence of Langevin dynamics for zero-sum games in probability distributions.

Zero-sum games such as chess and poker are, abstractly, functions that evaluate pairs of agents, for example labeling them `winner' and `loser'. If the game is approximately transitive, then self-play generates sequences of agents of increasing strength. However, nontransitive games, such as rock-paper-scissors, can ex…

Paper studies constrained control games with a novel approximation method.

Mutation improves FTRL convergence in zero-sum games.

The paper solves investment problems with uncertain factors using game theory.

Study learns optimal strategies in imperfect information games with self-play.

Algorithm learns Nash equilibria in stochastic games using entropy-regularized policies.

We study a wide class of non-convex non-concave min-max games that generalizes over standard bilinear zero-sum games. In this class, players control the inputs of a smooth function whose output is being applied to a bilinear zero-sum game. This class of games is motivated by the indirect nature of the competition in Ge…

In this paper we investigate the Follow the Regularized Leader dynamics in sequential imperfect information games (IIG). We generalize existing results of Poincaré recurrence from normal-form games to zero-sum two-player imperfect information games and other sequential game settings. We then investigate how adapting th…

Paper studies zero-sum games with noisy observations and identifies equilibrium conditions.

Paper develops efficient algorithms for zero-sum Markov games with general function classes.

Study of $2 imes 2$ zero-sum games with noisy observations and commitments.

We consider two-player non-zero-sum stopping games in discrete time. Unlike Dynkin games, in our games the payoff of each player is revealed after both players stop. Moreover, each player can adjust her own stopping strategy according to the other player's action. In the first part of the paper, we consider the game wh…

Zero-sum games have long guided artificial intelligence research, since they possess both a rich strategy space of best-responses and a clear evaluation metric. What's more, competition is a vital mechanism in many real-world multi-agent systems capable of generating intelligent innovations: Darwinian evolution, the ma…

New algorithms converge faster to Nash equilibrium in zero-sum games with bandit feedback.

Optimal algorithm for two-player zero-sum games with linear parameterization.

We consider a zero-sum continuous time stopping game in which the pay-off is revealed in the maximum of the two stopping times instead of the minimum, which is the case in Dynkin games.

Generative adversarial networks (GANs) represent a zero-sum game between two machine players, a generator and a discriminator, designed to learn the distribution of data. While GANs have achieved state-of-the-art performance in several benchmark learning tasks, GAN minimax optimization still poses great theoretical and…

Paper solves complex game theory problems with new equations.

This paper studies a 2-players zero-sum Dynkin game arising from pricing an option on an asset whose rate of return is unknown to both players. Using filtering techniques we first reduce the problem to a zero-sum Dynkin game on a bi-dimensional diffusion $(X,Y)$. Then we characterize the existence of a Nash equilibrium…

Pessimistic model-based algorithm finds Nash equilibria in zero-sum Markov games from offline data.

Paper analyzes robust strategies in a pension plan game with ambiguous financial markets.

Algorithm learns NE in imperfect information games with imperfect feedback.

Transformers learn to play games in-context, proving Nash equilibrium.

New algorithm improves sample efficiency for zero-sum Markov games.

We study the problem of repeated play in a zero-sum game in which the payoff matrix may change, in a possibly adversarial fashion, on each round; we call these Online Matrix Games. Finding the Nash Equilibrium (NE) of a two player zero-sum game is core to many problems in statistics, optimization, and economics, and fo…

Gradient-based methods for games suffer from discrete update steps that cause drift, affecting performance.

A geometric approach to differential game theory is illustrated. The parallel pursuit is considered as a two-player zero-sum differential game. The optimal strategies of each player is designed based on Riemann-Finsler geometry. Our approach incorporates a closed loop optimal control and the presentation is familiar wi…

Min-max formulations have attracted great attention in the ML community due to the rise of deep generative models and adversarial methods, while understanding the dynamics of gradient algorithms for solving such formulations has remained a grand challenge. As a first step, we restrict to bilinear zero-sum games and giv…

We formulate a general framework for competitive gradient-based learning that encompasses a wide breadth of multi-agent learning algorithms, and analyze the limiting behavior of competitive gradient-based learning algorithms using dynamical systems theory. For both general-sum and potential games, we characterize a non…

Unified framework for estimating reward functions in competitive games.

Game-theoretic models of learning are a powerful set of models that optimize multi-objective architectures. Among these models are zero-sum architectures that have inspired adversarial learning frameworks. An important shortcoming of these zeros-sum architectures is that gradient-based training leads to weak convergenc…

The paper analyzes strategic interactions in a multi-agent reinsurance chain using game theory.