Related papers: Solution to Zero-Sum Differential Game with Fracti…

This paper addresses a continuous-time risk-minimizing two-player zero-sum stochastic differential game (SDG), in which each player aims to minimize its probability of failure. Failure occurs in the event when the state of the game enters…

This paper addresses the problem of steering a discrete-time linear dynamical system from an initial Gaussian distribution to a final distribution in a game-theoretic setting. One of the two players strives to minimize a quadratic payoff,…

We study two-player zero-sum stochastic games, and propose a form of independent learning dynamics called Doubly Smoothed Best-Response dynamics, which integrates a discrete and doubly smoothed variant of the best-response dynamics into…

In this paper we study continuous-time two-player zero-sum optimal switching games on a finite horizon. Using the theory of doubly reflected BSDEs with interconnected barriers, we show that this game has a value and an equilibrium in the…

We study a problem of optimal irreversible investment and emission reduction formulated as a nonzero-sum dynamic game between an investor with environmental preferences and a firm. The game is set in continuous time on an infinite-time…

Differential game theory offers an approach for modeling interactions between two or more agents that occur in continuous time. The goal of each agent is to optimize its objective cost functional. In this paper, we present two different…

This work studies an algorithm, which we call magnetic mirror descent, that is inspired by mirror descent and the non-Euclidean proximal gradient algorithm. Our contribution is demonstrating the virtues of magnetic mirror descent as both an…

We develop an approach for two player constraint zero-sum and nonzero-sum stochastic differential games, which are modeled by Markov regime-switching jump-diffusion processes. We provide the relations between a usual stochastic optimal…

There has recently been considerable interest in using a nonstandard piecewise approximation to formulate fractional order differential equations as difference equations that describe the same dynamical behaviour and are more amenable to a…

In the present work, we consider 2-person zero-sum stochastic differential games with a nonlinear pay-off functional which is defined through a backward stochastic differential equation. Our main objective is to study for such a game the…

The Ultimatum Game is a famous sequential, two-player game intensely studied in Game Theory. A proposer can offer a certain fraction of some amount of a valuable good, for example, money. A responder can either accept, in which case the…

This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…

In this work, we investigate a security game between an attacker and a defender, originally proposed in \cite{emadi2019security}. As is well known, the combinatorial nature of security games leads to a large cost matrix. Therefore,…

We study online optimization methods for zero-sum games, a fundamental problem in adversarial learning in machine learning, economics, and many other domains. Traditional methods approximate Nash equilibria (NE) using either regret-based…

We consider a general type of non-Markovian impulse control problems under adverse non-linear expectation or, more specifically, the zero-sum game problem where the adversary player decides the probability measure. We show that the upper…

Zero-sum games arise in a wide variety of problems, including robust optimization and adversarial learning. However, algorithms deployed for finding a local Nash equilibrium in these games often converge to non-Nash stationary points. This…

We develop provably efficient reinforcement learning algorithms for two-player zero-sum finite-horizon Markov games with simultaneous moves. To incorporate function approximation, we consider a family of Markov games where the reward…

The article provides upper bounds for the blow-up time of a system of fractional differential equations in the Caputo sense. Furthermore, concrete examples of blow-up time estimation are given using a numerical algorithm of the…

A new solution concept for two-player zero-sum matrix games with multi-dimensional payoff is introduced. It is based on extensions of vector orders in K-dimensional spaces to order relations in their power sets, so-called set relations, and…

This paper considers a formulation of a differential game with constrained dynamics, where one player selects the dynamics and the other selects the applicable cost. When the game is considered on a finite time horizon, its value satisfies…