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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

In this paper we consider non zero-sum games where multiple players control the drift of a process, and their payoffs depend on its ergodic behaviour. We establish their connection with systems of Ergodic BSDEs, and prove the existence of a…

Probability · Mathematics 2017-06-16 Samuel N. Cohen , Victor Fedyashov

This paper is related to nonzero-sum stochastic differential games in the Markovian framework. We show existence of a Nash equilibrium point for the game when the drift is no longer bounded and only satisfies a linear growth condition. The…

Optimization and Control · Mathematics 2014-08-06 Said Hamadène , Rui Mu

In this paper, we study a class of discrete-time mean-field games under the infinite-horizon risk-sensitive discounted-cost optimality criterion. Risk-sensitivity is introduced for each agent (player) via an exponential utility function. In…

Optimization and Control · Mathematics 2018-10-08 Naci Saldi , Tamer Basar , Maxim Raginsky

In this paper, we investigate a partially observable zero sum games where the state process is a discrete time Markov chain. We consider a general utility function in the optimization criterion. We show the existence of value for both…

Optimization and Control · Mathematics 2022-11-16 Arnab Bhabak , Subhamay saha

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

We consider a nonzero-sum N-player Markov game on an abstract measurable state space with compact metric action spaces. The payoff functions are bounded Carath\'eodory functions and the transitions of the system are assumed to have a…

Optimization and Control · Mathematics 2023-05-09 François Dufour , Tomás Prieto-Rumeau

This paper investigates an inhomogeneous non-zero-sum linear-quadratic (LQ, for short) differential game problem whose state process and cost functional are regulated by a Markov chain. Under the $L^2$ stabilizability framework, we first…

Optimization and Control · Mathematics 2024-05-17 Fan Wu , Xun Li , Xin Zhang

We introduce and study a class of infinite-horizon non-zero-sum non-cooperative stochastic games with infinitely many interacting agents using ideas of statistical mechanics. First we show, in the general case of asymmetric interactions,…

Probability · Mathematics 2007-08-16 Emilio De Santis , Carlo Marinelli

A general class of mean field games are considered where the governing dynamics are controlled diffusions in $\mathbb{R}^d$. The optimization criterion is the long time average of a running cost function. Under various sets of hypotheses,…

Optimization and Control · Mathematics 2019-08-21 Ari Arapostathis , Anup Biswas , Johnson Carroll

We study infinite-horizon discounted two-player zero-sum Markov games, and develop a decentralized algorithm that provably converges to the set of Nash equilibria under self-play. Our algorithm is based on running an Optimistic Gradient…

Machine Learning · Computer Science 2021-07-08 Chen-Yu Wei , Chung-Wei Lee , Mengxiao Zhang , Haipeng Luo

We consider a large family of discrete and continuous time controlled Markov processes and study an ergodic risk-sensitive minimization problem. Under a blanket stability assumption, we provide a complete analysis to this problem. In…

Optimization and Control · Mathematics 2022-07-18 Anup Biswas , Somnath Pradhan

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

In this paper, we consider discrete-time dynamic games of the mean-field type with a finite number $N$ of agents subject to an infinite-horizon discounted-cost optimality criterion. The state space of each agent is a locally compact Polish…

Systems and Control · Computer Science 2017-01-17 Naci Saldi , Tamer Başar , Maxim Raginsky

One of the most classical games for stochastic processes is the zero-sum Dynkin (stopping) game. We present a complete equilibrium solution to a general formulation of this game with an underlying one-dimensional diffusion. A key result is…

Probability · Mathematics 2024-12-13 Sören Christensen , Kristoffer Lindensjö

The mathematical characterization of social-distancing games in classical epidemic theory remains an important question, for their applications to both infectious-disease theory and memetic theory. We consider a special case of the dynamic…

Computer Science and Game Theory · Computer Science 2026-03-16 Connor D Olson , Timothy C Reluga

In this paper, we consider discrete-time partially observed mean-field games with the risk-sensitive optimality criterion. We introduce risk-sensitivity behaviour for each agent via an exponential utility function. In the game model, each…

Systems and Control · Electrical Eng. & Systems 2022-11-11 Naci Saldi , Tamer Basar , Maxim Raginsky

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

We study the infinite horizon discrete time N-player nonzero-sum Dynkin game ($N \geq 2$) with stopping times as strategies (or pure strategies). We prove existence of an $\varepsilon$-Nash equilibrium point for the game by presenting a…

Optimization and Control · Mathematics 2022-03-10 Said Hamadène , Mohammed Hassani , Marie-Amélie Morlais

Stochastic games are an important class of problems that generalize Markov decision processes to game theoretic scenarios. We consider finite state two-player zero-sum stochastic games over an infinite time horizon with discounted rewards.…

Optimization and Control · Mathematics 2008-06-17 Parikshit Shah , Pablo A. Parrilo