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We study two-player zero-sum stopping games in continuous time and infinite horizon. We prove that the value in randomized stopping times exists as soon as the payoff processes are right-continuous. In particular, as opposed to existing…

Optimization and Control · Mathematics 2007-05-23 Rida Laraki , Eilon Solan

We prove that every two-player nonzero-sum stopping game in discrete time admits an \epsilon-equilibrium in randomized strategies for every \epsilon >0. We use a stochastic variation of Ramsey's theorem, which enables us to reduce the…

Probability · Mathematics 2007-05-23 Eran Shmaya , Eilon Solan

We study a general formulation of the classical two-player Dynkin game in a discrete time Markovian setting. We identify an appropriate class of mixed strategies -- \textit{Markovian randomized stopping times} -- in which players stop at…

Probability · Mathematics 2025-08-13 Sören Christensen , Kristoffer Lindensjö , Berenice Anne Neumann

This paper investigates the two-person zero-sum stochastic games for piece-wise deterministic Markov decision processes with risk-sensitive finite-horizon cost criterion on a general state space. Here, the transition and cost/reward rates…

Optimization and Control · Mathematics 2024-05-15 Subrata Golui

A recent method for solving zero-sum partially observable stochastic games (zs-POSGs) embeds the original game into a new one called the occupancy Markov game. This reformulation allows applying Bellman's principle of optimality to solve…

Computer Science and Game Theory · Computer Science 2024-06-04 Erwan Escudie , Matthia Sabatelli , Jilles Dibangoye

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 first study an optimal stopping problem in which a player (an agent) uses a discrete stopping time in order to stop optimally a payoff process whose risk is evaluated by a (non-linear) $g$-expectation. We then consider a non-zero-sum…

Probability · Mathematics 2017-05-11 Miryana Grigorova , Marie-Claire Quenez

We consider the general model of zero-sum repeated games (or stochastic games with signals), and assume that one of the players is fully informed and controls the transitions of the state variable. We prove the existence of the uniform…

Optimization and Control · Mathematics 2009-04-20 Jérôme Renault

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

We consider 2-player zero-sum stochastic games where each player controls his own state variable living in a compact metric space. The terminology comes from gambling problems where the state of a player represents its wealth in a casino.…

Optimization and Control · Mathematics 2017-02-23 Rida Laraki , Jérôme Renault

We study nonzero-sum stochastic games for continuous time Markov decision processes on a denumerable state space with risk-sensitive ergodic cost criterion. Transition rates and cost rates are allowed to be unbounded. Under a Lyapunov type…

Optimization and Control · Mathematics 2022-07-18 Mrinal K Ghosh , Subrata Golui , Chandan Pal , Somnath Pradhan

We study a finite-horizon two-person zero-sum risk-sensitive stochastic game for continuous-time Markov chains and Borel state and action spaces, in which payoff rates, transition rates and terminal reward functions are allowed to be…

Optimization and Control · Mathematics 2021-03-09 Junyu Zhang , Xianping Guo , Li Xia

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

In a probabilistic mean field game driven by a L\'evy process an individual player aims to minimize a long run discounted/ergodic cost by controlling the process through a pair of increasing and decreasing c\`adl\`ag processes, while he is…

Optimization and Control · Mathematics 2025-05-30 Facundo Oliú

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 consider zero-sum stochastic games for continuous time Markov decision processes with risk-sensitive average cost criterion. Here the transition and cost rates may be unbounded. We prove the existence of the value of the game and a…

Optimization and Control · Mathematics 2021-09-21 Mrinal K. Ghosh , Subrata Golui , Chandan Pal , Somnath Pradhan

We study a zero-sum game where the evolution of a spectrally one-sided Levy process is modified by a singular controller and is terminated by the stopper. The singular controller minimizes the expected values of running, controlling and…

Optimization and Control · Mathematics 2014-08-08 Daniel Hernandez-Hernandez , Kazutoshi Yamazaki

While single-agent policy optimization in a fixed environment has attracted a lot of research attention recently in the reinforcement learning community, much less is known theoretically when there are multiple agents playing in a…

Machine Learning · Computer Science 2022-07-27 Shuang Qiu , Xiaohan Wei , Jieping Ye , Zhaoran Wang , Zhuoran Yang

In this paper we establish a new connection between a class of 2-player nonzero-sum games of optimal stopping and certain $2$-player nonzero-sum games of singular control. We show that whenever a Nash equilibrium in the game of stopping is…

Optimization and Control · Mathematics 2017-12-29 Tiziano De Angelis , Giorgio Ferrari

In this paper we study the nonzero-sum Dynkin game in continuous time which is a two player non-cooperative game on stopping times. We show that it has a Nash equilibrium point for general stochastic processes. As an application, we…

Pricing of Securities · Quantitative Finance 2008-12-10 Said Hamadene , Jianfeng Zhang