arXiv research

The existence of stationary Markov perfect equilibria in stochastic games is shown under a general condition called "(decomposable) coarser transition kernels". This result covers various earlier existence results on correlated equilibria, noisy stochastic games, stochastic games with finite actions and state-independe…

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

New method improves convergence for smooth games.

The paper solves investment problems with uncertain factors using game theory.

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

In this paper we propose and analyze a class of $N$-player stochastic games that include finite fuel stochastic games as a special case. We first derive sufficient conditions for the Nash equilibrium (NE) in the form of a verification theorem. The associated Quasi-Variational-Inequalities include an essential game comp…

Do you remember your first video game console? We remember ours. Decades ago, they provided hours of entertainment. Now, we have repurposed them to solve dynamic and stochastic optimization problems. With deep reinforcement learning methods posting superhuman performance on a wide range of Atari games, we consider the …

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

Paper proves existence and uniqueness of solutions to nonlocal systems, generalizing stochastic game theory.

Graphon game model simplifies stochastic interactions among agents.

This paper studies insurers' robust strategies in a stochastic game with model uncertainty and volatility risk.

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…

Paper studies competitive networks where teams aim to minimize their own objectives, adapting to each other's strategies.

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

Solves a game between brokers and informed traders using stochastic differential equations.

Paper solves complex game theory problems with new equations.

Omega method mitigates noise in stochastic game optimization.

Two-layer model studies reinsurance contracts and competition between insurer and reinsurers.

We study optimal behavior of energy producers under a CO_2 emission abatement program. We focus on a two-player discrete-time model where each producer is sequentially optimizing her emission and production schedules. The game-theoretic aspect is captured through a reduced-form price-impact model for the CO_2 allowance…

The paper extends macroscopic market making to stochastic games, revealing properties and solving equations.

Paper presents a GMFG framework for large stochastic games.

Study competitive energy markets using stochastic impulse games.

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…

Proves minimax sample complexity for turn-based stochastic games.

Financial markets are often driven by latent factors which traders cannot observe. Here, we address an algorithmic trading problem with collections of heterogeneous agents who aim to perform optimal execution or statistical arbitrage, where all agents filter the latent states of the world, and their trading actions hav…

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

Game theory model shows optimal investment strategy for wealth growth.

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

Study optimizes SREC generation and trading in solar energy markets.

Even when confronted with the same data, agents often disagree on a model of the real-world. Here, we address the question of how interacting heterogenous agents, who disagree on what model the real-world follows, optimize their trading actions. The market has latent factors that drive prices, and agents account for th…

Improves GANs training through game theory.

We extend the stochastic Perron method to analyze the framework of stochastic target games, in which one player tries to find a strategy such that the state process almost surely reaches a given target no matter which action is chosen by the other player. Within this framework, our method produces a viscosity sub-solut…

Study on games with degenerate diffusion matrices, proving value existence and convergence.

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…

In this article we consider a game theoretic approach to the Risk-Sensitive Benchmarked Asset Management problem (RSBAM) of Davis and Lleo \cite{DL}. In particular, we consider a stochastic differential game between two players, namely, the investor who has a power utility while the second player represents the market …

Model strategic interactions between market makers and traders to optimize execution.

Study of LQ MFGs in infinite-dimensional Hilbert spaces.

The paper analyzes trade execution strategies for large traders in a stochastic market environment.

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…

New convergence guarantees for SGDA and SCO under expected co-coercivity.

In this paper, we settle the sampling complexity of solving discounted two-player turn-based zero-sum stochastic games up to polylogarithmic factors. Given a stochastic game with discount factor $γ\in(0,1)$ we provide an algorithm that computes an $ε$-optimal strategy with high-probability given $\tilde{O}((1 - γ)^{-3}…

EigenGame improves eigendecomposition by offering unbiased updates for larger datasets.

Stochastic games provide a framework for interactions among multiple agents and enable a myriad of applications. In these games, agents decide on actions simultaneously, the state of every agent moves to the next state, and each agent receives a reward. However, finding an equilibrium (if exists) in this game is often …

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

APAC-Net solves high-dimensional stochastic MFGs using neural networks.

We consider the problem of two-player zero-sum games. This problem is formulated as a min-max Markov game in the literature. The solution of this game, which is the min-max payoff, starting from a given state is called the min-max value of the state. In this work, we compute the solution of the two-player zero-sum game…

We consider a zero-sum stochastic differential controller-and-stopper game in which the state process is a controlled diffusion evolving in a multi-dimensional Euclidean space. In this game, the controller affects both the drift and the volatility terms of the state process. Under appropriate conditions, we show that t…

The paper extends game theory using Hodge theory on graphs.