arXiv research

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

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

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

Study on local convergence of min-max algorithms to differential equilibria on Riemannian manifolds.

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

We consider $n$ risk-averse agents who compete for liquidity in an Almgren--Chriss market impact model. Mathematically, this situation can be described by a Nash equilibrium for a certain linear-quadratic differential game with state constraints. The state constraints enter the problem as terminal boundary conditions f…

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

Investigates time-inconsistent portfolio selection under MMV preferences.

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

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

Proposes a deep learning method for solving complex financial games with delays.

The paper solves TIC LQ control problems using stochastic differential games.

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

Study on optimal trading in a finite population with market frictions and asymmetric information.

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

In this paper, we apply the idea of fictitious play to design deep neural networks (DNNs), and develop deep learning theory and algorithms for computing the Nash equilibrium of asymmetric $N$-player non-zero-sum stochastic differential games, for which we refer as \emph{deep fictitious play}, a multi-stage learning pro…

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…

This paper develops a new methodology for studying continuous-time Nash equilibrium in a financial market with asymmetrically informed agents. This approach allows us to lift the restriction of risk neutrality imposed on market makers by the current literature. It turns out that, when the market makers are risk averse,…

We analyze a market impact game between $n$ risk averse agents who compete for liquidity in a market impact model with permanent price impact and additional slippage. Most market parameters, including volatility and drift, are allowed to vary stochastically. Our first main result characterizes the Nash equilibrium in t…

Modeling market makers' quoting strategies to understand price impact.

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…

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…

Investors' strategic trading affects asset prices, modeled as a game.

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.

PAPAL algorithm finds mixed Nash equilibria in continuous games.

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

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

We propose a model of inter-bank lending and borrowing which takes into account clearing debt obligations. The evolution of log-monetary reserves of $N$ banks is described by coupled diffusions driven by controls with delay in their drifts. Banks are minimizing their finite-horizon objective functions which take into a…

Policy gradient methods find Nash equilibrium in noisy games.

EigenGame reinterprets PCA as a game to find eigenvectors.

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

Game theory models how agents trade in a risky asset considering price impact and a common signal.

Proves minimax sample complexity for turn-based stochastic games.

Transient market impact explained via Nash equilibrium in a game.

A game-theoretic analysis of DEX competition through dynamic trading fees.

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

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

In his lectures at College de France, P.L. Lions introduced the concept of Master equation, see [5] for Mean Field Games. It is introduced in a heuristic fashion, from the system of partial differential equations, associated to a Nash equilibrium for a large, but finite, number of players. The method, also explained in…

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 characterizes equilibrium strategies for stochastic control with higher-order moments.

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 …

UBI model proves financial equilibrium exists.

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.

Study competitive energy markets using stochastic impulse games.