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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

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…

Optimization and Control · Mathematics 2009-09-25 Rami Atar , Paul Dupuis

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

We study a differential game where two players separately control their own dynamics, pay a running cost, and moreover pay an exit cost (quitting the game) when they leave a fixed domain. In particular, each player has its own domain and…

Optimization and Control · Mathematics 2019-10-16 Fabio Bagagiolo , Rosario Maggistro , Marta Zoppello

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

For a non-cooperative differential game, the value functions of the various players satisfy a system of Hamilton-Jacobi equations. In the present paper, we consider a class of infinite-horizon games with nonlinear costs exponentially…

Analysis of PDEs · Mathematics 2014-08-07 Alberto Bressan , Fabio S. Priuli

In this paper, we consider state and control path-dependent stochastic zero-sum differential games, where the dynamics and the running cost include both state and control paths of the players. Using the notion of nonanticipative strategies,…

Optimization and Control · Mathematics 2021-02-10 Jun Moon

This paper analyses a stochastic differential game of control and stopping in which one of the players modifies a diffusion process using impulse controls, an adversary then chooses a stopping time to end the game. The paper firstly…

Optimization and Control · Mathematics 2019-10-04 David Mguni

We consider zero-sum stochastic differential games with possibly path-dependent controlled state. Unlike the previous literature, we allow for weak solutions of the state equation so that the players' controls are automatically of feedback…

Probability · Mathematics 2018-08-14 Dylan Possamaï , Nizar Touzi , Jianfeng Zhang

In this paper we investigate two-player zero-sum stochastic differential games with an ergodic payoff, in which the diffusion coefficient does not need to be non-degenerate. We first establish the existence of a viscosity solution to the…

Optimization and Control · Mathematics 2026-01-21 Juan Li , Wenqiang Li , Yanwei Li , Huaizhong Zhao

This paper is concerned with the controller-and-stopper stochastic differential game under a regime switching model in an infinite horizon. The state of the system consists of a number of diffusions \emph{coupled} by a continuous-time…

Optimization and Control · Mathematics 2021-11-02 Siyu Lv

For a non-cooperative m-persons differential game, the value functions ofthe various players satisfy a system of Hamilton-Jacobi-Bellman equations.Nashequilibrium solutions in feedback form can be obtained by studying a related system of…

Optimization and Control · Mathematics 2009-01-31 Jaykov Foukzon

We analyze a zero-sum stochastic differential game between two competing players who can choose unbounded controls. The payoffs of the game are defined through backward stochastic differential equations. We prove that each player's priority…

Probability · Mathematics 2013-03-14 Erhan Bayraktar , Song Yao

We consider stochastic impulse control problems when the impulses cost functions are arbitrary. We use the dynamic programming principle and viscosity solutions approach to show that the value function is a unique viscosity solution for the…

Optimization and Control · Mathematics 2019-01-17 Brahim El Asri , Sehail Mazid

This investigation is dedicated to a two-player zero-sum stochastic differential game (SDG), where a cost function is characterized by a backward stochastic differential equation (BSDE) with a continuous and monotonic generator regarding…

Optimization and Control · Mathematics 2024-04-19 Guangchen Wang , Zhuangzhuang Xing

For a zero-sum stochastic game which does not satisfy the Isaacs condition, we provide a value function representation for an Isaacs-type equation whose Hamiltonian lies in between the lower and upper Hamiltonians, as a convex combination…

Probability · Mathematics 2016-09-30 Daniel Hernández-Hernández , Mihai Sîrbu

We investigate a two-player zero-sum stochastic differential game problem with the state process being constrained in a connected bounded closed domain, and the cost functional described by the solution of a generalized backward stochastic…

Probability · Mathematics 2017-05-12 Lishun Xiao , Dejian Tian

We study a finite-horizon differential game of pursuit-evasion like, between a single player and a mass of agents. The player and the mass directly control their own evolution, which for the mass is given by a first order PDE of transport…

Optimization and Control · Mathematics 2025-02-28 Fabio Bagagiolo , Rossana Capuani , Luciano Marzufero

We study a zero-sum stochastic differential switching game in infinite horizon. We prove the existence of the value of the game and characterize it as the unique viscosity solution of the associated system of quasi-variational inequalities…

Optimization and Control · Mathematics 2018-05-04 Brahim El Asri , Sehail Mazid

This paper develops an algorithm for upper- and lower-bounding the value function for a class of linear time-varying games subject to convex control sets. In particular, a two-player zero-sum differential game is considered where the…

Optimization and Control · Mathematics 2025-03-12 Vincent Liu , Chris Manzie , Peter M. Dower