arXiv research

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

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.

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…

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

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

PAPAL algorithm finds mixed Nash equilibria in continuous games.

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

Policy gradient methods find Nash equilibrium in noisy games.

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

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.

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.

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…

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

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 …

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…

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.

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…

New systemic risk models for banks choosing their group memberships.

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

Paper analyzes strategic underreporting in competitive insurance markets.

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…

Study equilibrium consumption habits in a large population using mean field games.

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 [$…

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

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

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…

We study the high-frequency limits of strategies and costs in a Nash equilibrium for two agents that are competing to minimize liquidation costs in a discrete-time market impact model with exponentially decaying price impact and quadratic transaction costs of size $θ\ge0$. We show that, for $θ=0$, equilibrium strategie…

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…

Investors' strategies in a market influenced by price impact are analyzed, showing aggressive behavior when impact exceeds a critical point.

Study Nash equilibria in mean field portfolio games with consumption.

Investigates portfolio selection among competitive agents with mean-variance preferences.

Improves GANs training through game theory.

This article presents a proof of the existence of Bertrand-Nash equilibrium prices with multi-product firms and under the Logit model of demand that does not rely on restrictive assumptions on product characteristics, firm homogeneity or symmetry, product costs, or linearity of the utility function. The proof is based …

In this paper, we analyze Nash equilibria 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 production. We set out a…

Algorithm finds Nash equilibria in complex games with function approximation.

We consider the problem of finding Nash equilibrium for two-player turn-based zero-sum games. Inspired by the AlphaGo Zero (AGZ) algorithm, we develop a Reinforcement Learning based approach. Specifically, we propose Explore-Improve-Supervise (EIS) method that combines "exploration", "policy improvement"' and "supervis…

A Systemic Optimal Risk Transfer Equilibrium (SORTE) was introduced in: "Systemic optimal risk transfer equilibrium", Mathematics and Financial Economics (2021), for the analysis of the equilibrium among financial institutions or in insurance-reinsurance markets. A SORTE conjugates the classical Bühlmann's notion of a …

A new method for RLHF using proximal point Nash learning.

Motivated by the scarcity of accurate payoff feedback in practical applications of game theory, we examine a class of learning dynamics where players adjust their choices based on past payoff observations that are subject to noise and random disturbances. First, in the single-player case (corresponding to an agent tryi…