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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

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

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

Zero-sum stochastic games have found important applications in a variety of fields, from machine learning to economics. Work on this model has primarily focused on the computation of Nash equilibrium due to its effectiveness in solving…

Computer Science and Game Theory · Computer Science 2022-11-28 Denizalp Goktas , Jiayi Zhao , Amy Greenwald

Motivated by a vaccination coverage problem, we consider here a zero-sum differential game governed by a differential system consisting of a hyperbolic partial differential equation (PDE) and an ordinary differential equation (ODE). Two…

Analysis of PDEs · Mathematics 2024-12-18 Mauro Garavello , Elena Rossi , Abraham Sylla

This paper aims at investigating the problem of fast convergence to the Nash equilibrium (NE) for N-Player noncooperative differential games. The proposed method is such that the players attain their NE point without steady-state…

Optimization and Control · Mathematics 2023-01-13 Zahra Zahedi , Alireza Khayatian , Mohammad Mehdi Arefi , Shen Yin

We study two person nonzero-sum stochastic differential games with risk-sensitive discounted and ergodic cost criteria. Under certain conditions we establish a Nash equilibrium in Markov strategies for the discounted cost criterion and a…

Optimization and Control · Mathematics 2016-04-06 Mrinal K. Ghosh , K. Suresh Kumar , Chandan Pal

We consider two-player zero-sum differential games (ZSDGs), where the state process (dynamical system) depends on the random initial condition and the state process's distribution, and the objective functional includes the state process's…

Optimization and Control · Mathematics 2020-05-26 Jun Moon , Tamer Basar

We consider a finite-horizon, zero-sum game in which both players control a stochastic differential equation by invoking impulses. We derive a control randomization formulation of the game and use the existence of a value for the randomized…

Optimization and Control · Mathematics 2025-05-13 Magnus Perninge

We show that an N-person non-cooperative semi-Markov game under limiting ratio average pay-off has a pure semi-stationary Nash equilibrium. In an earlier paper, the zero-sum two person case has been dealt with. The proof follows by reducing…

Computer Science and Game Theory · Computer Science 2024-02-27 K. G. Bakshi , S. Sinha

Static potential games are non-cooperative games which admit a fictitious function, also referred to as a potential function, such that the minimizers of this function constitute a subset (or a refinement) of the Nash equilibrium strategies…

Optimization and Control · Mathematics 2021-03-08 Aathira Prasad , Puduru Viswanadha Reddy

This work presents a novel policy iteration algorithm to tackle nonzero-sum stochastic impulse games arising naturally in many applications. Despite the obvious impact of solving such problems, there are no suitable numerical methods…

Optimization and Control · Mathematics 2020-06-29 René Aïd , Francisco Bernal , Mohamed Mnif , Diego Zabaljauregui , Jorge P. Zubelli

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 this paper, we consider a differential stochastic zero-sum game in which two players intervene by adopting impulse controls in a finite time horizon. We provide a numerical solution as an approximation of the value function, which turns…

Optimization and Control · Mathematics 2024-10-14 Antoine Zolome , Brahim El Asri

Nonzero-sum stochastic differential games with impulse controls offer a realistic and far-reaching modelling framework for applications within finance, energy markets, and other areas, but the difficulty in solving such problems has…

Numerical Analysis · Mathematics 2020-06-29 Diego Zabaljauregui

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 study a class of zero-sum two-player stochastic differential games with the controlled stochastic differential equations and the payoff/cost functionals of recursive type. As opposed to the pioneering work by Fleming and…

Probability · Mathematics 2021-05-21 Jinniao Qiu , Jing Zhang

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 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

In this paper, we consider two-player zero-sum matrix and stochastic games and develop learning dynamics that are payoff-based, convergent, rational, and symmetric between the two players. Specifically, the learning dynamics for matrix…

Machine Learning · Computer Science 2024-09-06 Zaiwei Chen , Kaiqing Zhang , Eric Mazumdar , Asuman Ozdaglar , Adam Wierman