arXiv research

PAPAL algorithm finds mixed Nash equilibria in continuous 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…

Method identifies mixed Nash equilibria in high dimensions for training mixtures of GANs.

By generalizing the measurements on the game experiments of mixed strategy Nash equilibrium, we study the dynamical pattern in a representative dynamic stochastic general equilibrium (DSGE). The DSGE model describes the entanglements of the three variables (output gap [$y$], inflation [$π$] and nominal interest rate [$…

Save for some special cases, current training methods for Generative Adversarial Networks (GANs) are at best guaranteed to converge to a `local Nash equilibrium` (LNE). Such LNEs, however, can be arbitrarily far from an actual Nash equilibrium (NE), which implies that there are no guarantees on the quality of the found…

We argue that the existing regret matchings for Nash equilibrium approximation conduct "jumpy" strategy updating when the probabilities of future plays are set to be proportional to positive regret measures. We propose a geometrical regret matching which features "smooth" strategy updating. Our approach is simple, intu…

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

The paper develops a new algorithm for constructing minimax estimators using online learning techniques.

No-regret learning fails to converge to Nash equilibria in mixed strategies.

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…

New algorithm for solving minimax problems over distributions converges to Nash equilibrium.

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

Optimizes pension mix of PAYGO, EET, and individual savings.

Study Nash competition among dealers quoting prices to clients with unknown trading motives.

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

Paper explores limits and possibilities of aligning LLMs with human preferences.

In this note, we present an existence result of a Nash equilibrium between electricity producers selling their production on an electricity market and buying CO2 emission allowances on an auction carbon market. The producers' strategies integrate the coupling of the two markets via the cost functions of the electricity…

Study Nash equilibrium between broker and trader in a lit exchange with price impact.

Improved SEG method converges to Nash equilibrium in bilinear games.

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

Study analyzes market equilibrium returns with price impact and transaction costs.

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

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

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

Policy gradient methods find Nash equilibrium in noisy games.

Deep neural network solves large multi-agent games for Markovian Nash equilibrium.

Paper studies convergence of Mean-Field GDA dynamics for MNE of continuous games.

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

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…

Proposes a new training algorithm for zero-sum games to avoid convergence issues.

Study Nash equilibrium between broker and informed trader in dealer and lit markets.

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

Study on hypothesis testing games with adversarial classification, showing convergence rates.

Investigates time-inconsistent portfolio selection under MMV preferences.

Proves minimax sample complexity for turn-based stochastic games.

Transient market impact explained via Nash equilibrium in a game.

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

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

Actor-critic finds Nash in mean-field games with linear-quadratic costs.

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 address the challenge of designing optimal adversarial noise algorithms for settings where a learner has access to multiple classifiers. We demonstrate how this problem can be framed as finding strategies at equilibrium in a two-player, zero-sum game between a learner and an adversary. In doing so, we illustrate the…

Paper tackles stochastic control with mean and higher-order moments, finding Nash equilibria.

Extends SORTE to multivariate risk functions.

We study an infinite-horizon discrete-time optimal stopping problem under non-exponential discounting. A new method, which we call the iterative approach, is developed to find subgame perfect Nash equilibria. When the discount function induces decreasing impatience, we establish the existence of an equilibrium through …

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

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

Market impact game analyzed with stochastic parameters using FBSDEs.

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…