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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

This paper presents a novel approach to numerically solve stochastic differential games for nonlinear systems. The proposed approach relies on the nonlinear Feynman-Kac theorem that establishes a connection between parabolic deterministic…

Optimization and Control · Mathematics 2019-06-13 Ziyi Wang , Keuntaek Lee , Marcus A. Pereira , Ioannis Exarchos , Evangelos A. Theodorou

In this paper we study zero-sum two-player stochastic differential games with jumps with the help of theory of Backward Stochastic Differential Equations (BSDEs). We generalize the results of Fleming and Souganidis [10] and those by Biswas…

Optimization and Control · Mathematics 2010-04-19 Rainer Buckdahn , Ying Hu , Juan Li

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…

Optimization and Control · Mathematics 2025-07-04 Craig Bakker , Adam T. Rupe , Alexander Von Moll , Adam R. Gerlach

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

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

Definable zero-sum stochastic games involve a finite number of states and action sets, reward and transition functions that are definable in an o-minimal structure. Prominent examples of such games are finite, semi-algebraic or globally…

Optimization and Control · Mathematics 2015-01-05 Jérôme Bolte , Stéphane Gaubert , Guillaume Vigeral

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

In this paper, we formulate a two-player zero-sum game under dynamic constraints defined by hybrid dynamical equations. The game consists of a min-max problem involving a cost functional that depends on the actions and resulting solutions…

Optimization and Control · Mathematics 2025-05-20 Santiago J. Leudo , Ricardo G. Sanfelice

We prove existence of a value for two-player zero-sum stopper vs. singular-controller games on finite-time horizon, when the underlying dynamics is one-dimensional, diffusive and bound to evolve in $[0,\infty)$. We show that the value is…

Optimization and Control · Mathematics 2025-06-26 Andrea Bovo , Tiziano De Angelis

In the Target-Attacker-Defender (TAD) differential game, an Attacker missile strives to capture a Target aircraft. The Target tries to escape the Attacker and is aided by a Defender missile which aims at intercepting the Attacker before the…

Optimization and Control · Mathematics 2020-02-12 Eloy Garcia , David W. Casbeer , Meir Pachter

Zero sum games with risk-sensitive cost criterion are considered with underlying dynamics being given by controlled stochastic differential equations. Under the assumption of geometric stability on the dynamics , we completely characterize…

Optimization and Control · Mathematics 2018-01-04 Anup Biswas , Subhamay Saha

We study a nonzero-sum stochastic differential game with both players adopting impulse controls, on a finite time horizon. The objective of each player is to maximize her total expected discounted profits. The resolution methodology relies…

Optimization and Control · Mathematics 2021-12-21 René Aïd , Lamia Ben Ajmia , M'hamed Gaïgi , Mohamed Mnif

We establish existence of nearly-optimal controls, conditions for existence of an optimal control and a saddle-point for respectively a control problem and zero-sum differential game associated with payoff functionals of mean-field type,…

Probability · Mathematics 2017-07-25 Boualem Djehiche , Said Hamadène

A general model for zero-sum stochastic games with asymmetric information is considered. In this model, each player's information at each time can be divided into a common information part and a private information part. Under certain…

Systems and Control · Electrical Eng. & Systems 2019-12-25 Dhruva Kartik , Ashutosh Nayyar

A fundamental task in mobile robotics is to keep an agent under surveillance using an autonomous robotic platform equipped with a sensing device. Using differential game theory, we study a particular setup of the previous problem. A…

Robotics · Computer Science 2024-09-16 Rodrigo Saavedra , Ubaldo Ruiz

In this paper, we consider a partial observed two-person zero-sum stochastic differential game problem where the system is governed by a stochastic differential equation of mean-field type. Under standard assumptions on the coefficients,…

Optimization and Control · Mathematics 2016-11-15 Maoning Tang , Qingxin Meng

This article introduces differential hybrid games, which combine differential games with hybrid games. In both kinds of games, two players interact with continuous dynamics. The difference is that hybrid games also provide all the features…

Logic in Computer Science · Computer Science 2017-08-17 André Platzer

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…

Optimization and Control · Mathematics 2018-06-04 Said Hamadène , Randall Martyr , John Moriarty

We study the asymptotic value of a frequency-dependent zero-sum game with separable payoff following a differential approach. The stage payoffs in such games depend on the current actions and on a linear function of the frequency of actions…

Optimization and Control · Mathematics 2019-01-23 Joseph Abdou , Nikolaos Pnevmatikos