arXiv research

New assumptions and algorithm solve offline two-player zero-sum Markov games.

Consider a two-player zero-sum stochastic game where the transition function can be embedded in a given feature space. We propose a two-player Q-learning algorithm for approximating the Nash equilibrium strategy via sampling. The algorithm is shown to find an $ε$-optimal strategy using sample size linear to the number …

Paper solves discounted stochastic games with near-optimal time and sample complexity.

A new algorithm calculates optimal strategies for two-player zero-sum games.

Gradient methods converge exponentially in concave network games.

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

Combinatorial two-player games have recently been applied to knot theory. Examples of this include the Knotting-Unknotting Game and the Region Unknotting Game, both of which are played on knot shadows. These are turn-based games played by two players, where each player has a separate goal to achieve in order to win the…

This work models GHG offset credit markets to find optimal strategies for market participants.

This paper introduces a new class of Dynkin games, where the two players are allowed to make their stopping decisions at a sequence of exogenous Poisson arrival times. The value function and the associated optimal stopping strategy are characterized by the solution of a backward stochastic differential equation. The pa…

Recent work in reinforcement learning demonstrated that learning solely through self-play is not only possible, but could also result in novel strategies that humans never would have thought of. However, optimization methods cast as a game between two players require careful tuning to prevent suboptimal results. Hence,…

A geometric approach to differential game theory is illustrated. The parallel pursuit is considered as a two-player zero-sum differential game. The optimal strategies of each player is designed based on Riemann-Finsler geometry. Our approach incorporates a closed loop optimal control and the presentation is familiar wi…

In this note, we study a class of stochastic control problems where the optimal strategies are described by two parameters. These include a subset of singular control, impulse control, and two-player stochastic games. The parameters are first chosen by the two continuous/smooth fit conditions, and then the optimality o…

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…

Optimal strategies are found for a repeated betting game using diffusion approximation.

New findings show pure strategy equilibria are more robust in a war of attrition game.

New game approximates mean curvature flow evolution.

Two strategic agents track their portfolios, influencing each other's trading targets.

New method learns optimal prediction strategies in adversarial games.

Study proposes new OPE estimators for two-player zero-sum games.

Adversarial self-play in two-player games has delivered impressive results when used with reinforcement learning algorithms that combine deep neural networks and tree search. Algorithms like AlphaZero and Expert Iteration learn tabula-rasa, producing highly informative training data on the fly. However, the self-play t…

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

New strategy achieves optimal regret without communication or collisions in multi-player bandit.

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 …

Novel approach finds implicit regularisation in two-player games using BEA.

DREAM learns optimal strategies in imperfect games without needing a simulator.

Two non-communicating players minimize regret in a multi-armed bandit game.

All people have to make risky decisions in everyday life. And we do not know how true they are. But is it possible to mathematically assess the correctness of our choice? This article discusses the model of decision making under risk on the example of project management. This is a game with two players, one of which is…

New algorithm finds near-optimal policies efficiently in zero-sum games.

RLCFR improves CFR's generalization in imperfect information games.

This paper studies a 2-players zero-sum Dynkin game arising from pricing an option on an asset whose rate of return is unknown to both players. Using filtering techniques we first reduce the problem to a zero-sum Dynkin game on a bi-dimensional diffusion $(X,Y)$. Then we characterize the existence of a Nash equilibrium…

Optimal adversarial noise algorithms for multiple classifiers using game theory.

Study learns optimal strategies in imperfect information games with self-play.

We reconsider the training objective of Generative Adversarial Networks (GANs) from the mixed Nash Equilibria (NE) perspective. Inspired by the classical prox methods, we develop a novel algorithmic framework for GANs via an infinite-dimensional two-player game and prove rigorous convergence rates to the mixed NE, reso…

New approach for adaptive conformal inference using Blackwell's theory.

Optimistic Hedge achieves optimal regret bounds in two-player zero-sum games.

Research tackles alliance formation in many-player zero-sum games, showing reinforcement learning fails but a contract mechanism can help.

Paper tackles multiplayer symmetric games, securing equal share for n players.

Gradient-based methods for games suffer from discrete update steps that cause drift, affecting performance.

Neural operators approximate Stackelberg game solutions.

The paper reveals a spinning top geometry in real-world games.

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

New RL method improves robustness across various conditions.

Game-theoretic analysis of mining gaps in blockchain systems.

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…

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

PAPAL algorithm finds mixed Nash equilibria in continuous games.

Paper solves complex game theory problems with new equations.

Classifiers can be trained with data-dependent constraints to satisfy fairness goals, reduce churn, achieve a targeted false positive rate, or other policy goals. We study the generalization performance for such constrained optimization problems, in terms of how well the constraints are satisfied at evaluation time, gi…