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We prove that for a class of zero-sum differential games with incomplete information on both sides, the value admits a probabilistic representation as the value of a zero-sum stochastic differential game with complete information, where…

Optimization and Control · Mathematics 2017-01-04 Fabien Gensbittel , Catherine Rainer

We develop here the Stochastic Perron Method in the framework of two-player zero-sum differential games. We consider the formulation of the game where both players play, symmetrically, feed-back strategies (as in [CR09] or [PZ12]) as…

Optimization and Control · Mathematics 2014-02-20 Mihai Sîrbu

We propose a framework for two-player infinite-dimensional games with cooperative or competitive structure. These games take the form of coupled partial differential equations in which players optimize over a space of measures, driven by…

Analysis of PDEs · Mathematics 2025-02-11 Lauren Conger , Franca Hoffmann , Eric Mazumdar , Lillian J. Ratliff

The value of a zero-sum differential games is known to exist, under Isaacs' condition, as the unique viscosity solution of a Hamilton-Jacobi-Bellman equation. In this note we provide a self-contained proof based on the construction of…

Optimization and Control · Mathematics 2013-01-29 Juan Pablo Maldonado López , Miquel Oliu-Barton

This article is dedicated to the study of mixed zero-sum two-player stochastic differential games in the situation when the player's cost functionals are modeled by doubly controlled reflected backward stochastic equations with two barriers…

Optimization and Control · Mathematics 2013-07-30 Said Hamadene , Eduard Rotenstein , Adrian Zalinescu

A zero-sum two person Perfect Information Stochastic game (PISG) under limiting average payoff has a value and both the maximiser and the minimiser have optimal pure stationary strategies. Firstly we form the matrix of undiscounted payoffs…

Optimization and Control · Mathematics 2023-02-15 K. G. Bakshi , S. Sinha

In this paper, we study an infinite horizon non-autonomous stochastic recursive differential game. To this end, we first establish well-posedness and stability results for BSDEs with a time-dependent discount factor and a possibly unbounded…

Optimization and Control · Mathematics 2026-05-14 Sheng Huang , Qingmeng Wei

In this paper we investigate zero-sum two-player stochastic differential games whose cost functionals are given by doubly controlled reflected backward stochastic differential equations (RBSDEs) with two barriers. For admissible controls…

Optimization and Control · Mathematics 2008-04-03 Rainer Buckdahn , Juan Li

In this paper, zero-sum mean-field type games (ZSMFTG) with linear dynamics and quadratic utility are studied under infinite-horizon discounted utility function. ZSMFTG are a class of games in which two decision makers whose utilities sum…

Optimization and Control · Mathematics 2020-09-07 René Carmona , Kenza Hamidouche , Mathieu Laurière , Zongjun Tan

We investigate an infinite dimensional partial differential equation of Isaacs' type, which arises from a zero-sum differential game between two masses. The evolution of the two masses is described by a controlled transport/continuity…

Optimization and Control · Mathematics 2025-05-07 Fabio Bagagiolo , Rossana Capuani , Luciano Marzufero

This paper presents Hamilton-Jacobi (HJ) formulations for two classes of two-player zero-sum games: one with a maximum cost value over time, and one with a minimum cost value over time. In the zero-sum game setting, player A minimizes the…

Optimization and Control · Mathematics 2021-06-30 Donggun Lee , Claire J. Tomlin

We consider a zero-sum stochastic differential game over elementary mixed feed-back strategies. These are strategies based only on the knowledge of the past state, randomized continuously in time from a sampling distribution which is kept…

Optimization and Control · Mathematics 2014-04-16 Mihai Sîrbu

In this paper we consider two-person zero-sum risk-sensitive stochastic dynamic games with Borel state and action spaces and bounded reward. The term risk-sensitive refers to the fact that instead of the usual risk neutral optimization…

Optimization and Control · Mathematics 2021-07-21 Nicole Bäuerle , Ulrich Rieder

In this paper we investigate Nash equilibrium payoffs for two-player nonzero-sum stochastic differential games whose cost functionals are defined by a system of coupled backward stochastic differential equations. We obtain an existence…

Probability · Mathematics 2014-01-21 Qian Lin

In this paper we find viscosity solutions to the two membranes problem (that is a system with two obstacle-type equations) with two different $p-$Laplacian operators taking limits of value functions of a sequence of games. We analyze…

Analysis of PDEs · Mathematics 2023-10-26 Alfredo Miranda , Julio D. Rossi

The paper deals with a zero-sum differential game in which the dynamical system is described by a fractional differential equation with the Caputo derivative of an order $\alpha \in (0, 1).$ The goal of the first (second) player is to…

Optimization and Control · Mathematics 2019-08-06 Mikhail Gomoyunov

This paper studies two-player zero-sum stochastic Bayesian games where each player has its own dynamic state that is unknown to the other player. Using typical techniques, we provide the recursive formulas and sufficient statistics in both…

Computer Science and Game Theory · Computer Science 2021-05-05 Nabiha Nasir Orpa , Lichun Li

We consider a two-player zero-sum game with integral payoff and with incomplete information on one side, where the payoff is chosen among a continuous set of possible payoffs. We prove that the value function of this game is solution of an…

Probability · Mathematics 2012-02-23 Pierre Cardaliaguet , Catherine Rainer

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…

Computer Science and Game Theory · Computer Science 2023-03-07 Zaiwei Chen , Kaiqing Zhang , Eric Mazumdar , Asuman Ozdaglar , Adam Wierman

This paper studies the mixed zero-sum stochastic differential game problem. We allow the functionals and dynamics to be of polynomial growth. The problem is formulated as an extended doubly reflected BSDEs with a specific generator. We show…

Probability · Mathematics 2021-03-05 Brahim El Asri , Nacer Ourkiya