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We study a two-player, zero-sum, dynamic game with incomplete information where one of the players is more informed than his opponent. We analyze the limit value as the players play more and more frequently. The more informed player…

Optimization and Control · Mathematics 2015-09-14 Fabien Gensbittel

We consider a zero-sum stochastic differential controller-and-stopper game in which the state process is a controlled diffusion evolving in a multi-dimensional Euclidean space. In this game, the controller affects both the drift and the…

Optimization and Control · Mathematics 2013-01-15 Erhan Bayraktar , Yu-Jui Huang

In this paper, we consider the functional It\^o calculus framework to find a path-dependent version of the Hamilton-Jacobi-Bellman equation for stochastic control problems that feature dynamics and running cost that depend on the path of…

Probability · Mathematics 2019-02-11 Yuri F. Saporito

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

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 consider an investment problem in which an investor performs capital injections to increase the liquidity of a firm for it to maximise profit from market operations. Each time the investor performs an injection, the investor incurs a…

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

We study a zero-sum stochastic differential game (SDG) in which one controller plays an impulse control while their opponent plays a stochastic control. We consider an asymmetric setting in which the impulse player commits to, at the start…

Probability · Mathematics 2019-01-31 Parsiad Azimzadeh

We study a class of zero-sum games between a singular-controller and a stopper over finite-time horizon. The underlying process is a multi-dimensional (locally non-degenerate) controlled stochastic differential equation (SDE) evolving in an…

Optimization and Control · Mathematics 2023-10-31 Andrea Bovo , Tiziano De Angelis , Elena Issoglio

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

We study a class of zero-sum stochastic games between a stopper and a singular-controller, previously considered in [Bovo and De Angelis (2025)]. The underlying singularly-controlled dynamics takes values in…

Optimization and Control · Mathematics 2025-06-25 Andrea Bovo , Alessandro Milazzo

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

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…

Probability · Mathematics 2014-07-29 Rainer Buckdahn , Juan Li , Marc Quincampoix

We present a modified version of the two-player "tug-of-war" game introduced by Peres, Schramm, Sheffield, and Wilson. This new tug-of-war game is identical to the original except near the boundary of the domain $\partial \Omega$, but its…

Analysis of PDEs · Mathematics 2011-08-30 Scott N. Armstrong , Charles K. Smart

In this paper we first investigate zero-sum two-player stochastic differential games with reflection with the help of theory of Reflected Backward Stochastic Differential Equations (RBSDEs). We will establish the dynamic programming…

Probability · Mathematics 2008-09-30 Rainer Buckdahn , Juan Li

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

We study zero-sum repeated games where the minimizing player has to pay a certain cost each time he changes his action. Our contribution is twofold. First, we show that the value of the game exists in stationary strategies, depending solely…

Optimization and Control · Mathematics 2021-10-29 Yevgeny Tsodikovich , Xavier Venel , Anna Zseleva

We study the smoothness of the upper and lower value functions of stochastic differential games in the framework of time-homogeneous (possibly degenerate) diffusion processes in a domain, under the assumption that the diffusion, drift and…

Analysis of PDEs · Mathematics 2013-11-26 Wei Zhou

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 investigate a novel finite-horizon linear-quadratic (LQ) feedback dynamic potential game with a priori unknown cost matrices played between two players. The cost matrices are revealed to the players sequentially, with the potential for…

Optimization and Control · Mathematics 2025-08-05 Yitian Chen , Timothy L. Molloy , Iman Shames

In this paper we use viscosity approach to provide an explicit solution to the problem of a two - player switching game. We characterize the switching regions which reduce the switching problem into one of finding a finite number of…

Optimization and Control · Mathematics 2025-04-22 Brahim El Asri , Magnoudéwa Paka