arXiv research

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

New method finds all Nash equilibria via vector optimization.

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

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…

Study Nash equilibria in mean field portfolio games with consumption.

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

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

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

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…

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…

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

A RL approach finds Nash equilibrium for turn-based zero-sum games.

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

Policy gradient methods find Nash equilibrium in noisy games.

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.

GANs may not have Nash equilibria, but proximal training can find solutions.

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

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.

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

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

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

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

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…

Improved SEG method converges to Nash equilibrium in bilinear games.

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

Algorithm converges to Nash equilibria in competitive games.

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…

Algorithm finds Nash equilibria in complex games with function approximation.

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

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

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

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…

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

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

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…

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…

The paper explores how regularization can lead to convergence in imperfect information games.

PAPAL algorithm finds mixed Nash equilibria in continuous games.

Agents trained with reinforcement learning deviate from Nash equilibrium in optimal execution game.

The game-theoretic risk management framework put forth in the precursor work "Towards a Theory of Games with Payoffs that are Probability-Distributions" (arXiv:1506.07368 [q-fin.EC]) is herein extended by algorithmic details on how to compute equilibria in games where the payoffs are probability distributions. Our appr…

Study shows how multiple traders can trade together without excessive price impact.

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…

Gradient methods converge exponentially in concave network games.

Data-driven modeling increasingly requires to find a Nash equilibrium in multi-player games, e.g. when training GANs. In this paper, we analyse a new extra-gradient method for Nash equilibrium finding, that performs gradient extrapolations and updates on a random subset of players at each iteration. This approach prova…