arXiv research

New method finds all Nash equilibria via vector optimization.

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

In this paper, we study the problem of learning the set of pure strategy Nash equilibria and the exact structure of a continuous-action graphical game with quadratic payoffs by observing a small set of perturbed equilibria. A continuous-action graphical game can possibly have an uncountable set of Nash euqilibria. We p…

Study Nash equilibria in mean field portfolio games with consumption.

We propose local symplectic surgery, a two-timescale procedure for finding local Nash equilibria in two-player zero-sum games. We first show that previous gradient-based algorithms cannot guarantee convergence to local Nash equilibria due to the existence of non-Nash stationary points. By taking advantage of the differ…

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

We show by counterexample that policy-gradient algorithms have no guarantees of even local convergence to Nash equilibria in continuous action and state space multi-agent settings. To do so, we analyze gradient-play in N-player general-sum linear quadratic games, a classic game setting which is recently emerging as a b…

In this paper we review our earlier work on quantum computing and the Nash Equilibrium, in particular, tracing the history of the discovery of new Nash Equilibria and then reviewing the ways in which quantum computing may be expected to generate new classes of Nash equilibria. We then extend this work through a substan…

Policy gradient methods find Nash equilibrium in noisy games.

Policy mirror ascent achieves Nash equilibrium in mean field games without a population generative model.

Deep fictitious play converges to Nash equilibrium in stochastic differential games.

Novel approach to Nash equilibrium in mean-field stochastic games with operator resolvents.

In this paper we use game theory to model poisoning attack scenarios. We prove the non-existence of pure strategy Nash Equilibrium in the attacker and defender game. We then propose a mixed extension of our game model and an algorithm to approximate the Nash Equilibrium strategy for the defender. We then demonstrate th…

The paper analyzes game theory in convertible contracts during liquidity events.

A Nash game theory approach allocates capital requirements among financial institutions.

The paper examines Nash equilibrium in GANs for stationary Gaussian processes.

Study analyzes portfolio liquidation games influenced by self-exciting order flow.

Study Nash equilibrium in mean field portfolio games with random market parameters.

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…

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…

New RL algorithms find SNE in Markov games with myopic followers.

Model-free learning for multi-agent stochastic games is an active area of research. Existing reinforcement learning algorithms, however, are often restricted to zero-sum games, and are applicable only in small state-action spaces or other simplified settings. Here, we develop a new data efficient Deep-Q-learning method…

Improves GANs training through game theory.

Gradient methods converge exponentially in concave network games.

Last-iterate guarantees for learning in co-coercive games under noisy feedback.

We propose a deep neural network-based algorithm to identify the Markovian Nash equilibrium of general large $N$-player stochastic differential games. Following the idea of fictitious play, we recast the $N$-player game into $N$ decoupled decision problems (one for each player) and solve them iteratively. The individua…

The study examines Nash equilibria in utility maximization games with multiplicative performance criteria.

PAPAL algorithm finds mixed Nash equilibria in continuous games.

Decentralized algorithm reduces regret and converges to Nash equilibrium in online congestion 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…

Proposes a new criterion for selecting Nash equilibria considering both utility and inequality.

Proves minimax sample complexity for turn-based stochastic games.

Study improves $L^{\infty}$ estimates and extreme value behavior in stochastic differential games.

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

Generative Adversarial Networks (GAN) have become one of the most successful frameworks for unsupervised generative modeling. As GANs are difficult to train much research has focused on this. However, very little of this research has directly exploited game-theoretic techniques. We introduce Generative Adversarial Netw…

Paper optimizes reinforcement learning in self-play games with reduced steps.

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

We consider the problem of finding stationary Nash equilibria (NE) in a finite discounted general-sum stochastic game. We first generalize a non-linear optimization problem from Filar and Vrieze [2004] to a $N$-player setting and break down this problem into simpler sub-problems that ensure there is no Bellman error fo…

Improved SEG method converges to Nash equilibrium in bilinear games.

This paper tackles global Nash equilibrium in non-convex multi-player games.

The paper explores game-theoretic alignment of LLMs with human preferences, finding limitations and conditions.

EigenGame reinterprets PCA as a game to find eigenvectors.

Algorithm converges to Nash equilibria in competitive games.

Algorithm finds Nash equilibria in complex games with function approximation.

The paper tackles Nash-regret minimization in congestion games with bandit feedback.

In this paper we study the nonzero-sum Dynkin game in continuous time which is a two player non-cooperative game on stopping times. We show that it has a Nash equilibrium point for general stochastic processes. As an application, we consider the problem of pricing American game contingent claims by the utility maximiza…

We study discrete-time mean-field Markov games with infinite numbers of agents where each agent aims to minimize its ergodic cost. We consider the setting where the agents have identical linear state transitions and quadratic cost functions, while the aggregated effect of the agents is captured by the population mean o…

Study of LQ MFGs in infinite-dimensional Hilbert spaces.