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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

In a single-state repeated game, zero-determinant strategies can unilaterally force functions of the payoffs to take values in particular closed intervals. When the explicit use of a determinant is absent from the analysis, they are instead…

Computer Science and Game Theory · Computer Science 2021-01-01 Mario Palasciano

A game-theoretic framework for time-inconsistent stopping problems where the time-inconsistency is due to the consideration of a non-linear function of an expected reward is developed. A class of mixed strategy stopping times that allows…

Optimization and Control · Mathematics 2020-01-23 Sören Christensen , Kristoffer Lindensjö

In this paper, we focus on the stochastic representation of a system of coupled Hamilton-Jacobi-Bellman-Isaacs (HJB-Isaacs (HJBI), for short) equations which is in fact a system of coupled Isaacs' type integral-partial differential…

Optimization and Control · Mathematics 2023-07-12 Sheng Luo , Wenqiang Li , Xun Li , Qingmeng Wei

We study a class of stochastic target games where one player tries to find a strategy such that the state process almost-surely reaches a given target, no matter which action is chosen by the opponent. Our main result is a geometric dynamic…

Probability · Mathematics 2015-02-03 Bruno Bouchard , Marcel Nutz

Recent results of Ye and Hansen, Miltersen and Zwick show that policy iteration for one or two player (perfect information) zero-sum stochastic games, restricted to instances with a fixed discount rate, is strongly polynomial. We show that…

Optimization and Control · Mathematics 2013-10-21 Marianne Akian , Stéphane Gaubert

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

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

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

Simple stochastic games are two-player zero-sum stochastic games with turn-based moves, perfect information, and reachability winning conditions. We present two new algorithms computing the values of simple stochastic games. Both of them…

Computer Science and Game Theory · Computer Science 2015-07-01 Hugo Gimbert , Florian Horn

We formulate a class of mean field games on a finite state space with variational principles resembling those in continuous-state mean field games. We construct a controlled continuity equation featuring a nonlinear activation function on…

Optimization and Control · Mathematics 2023-10-10 Yuan Gao , Wuchen Li , Jian-Guo Liu

We consider a stochastic game of contribution to the common good in which the players have continuous control over the degree of contribution, and we examine the gradualism arising from the free rider effect. This game belongs to the class…

Optimization and Control · Mathematics 2022-07-14 H. Dharma Kwon

We study two classes of zero-sum stochastic games with compact action sets and a finite product state space. These two classes assume a communication property on the state spaces of the players. For strongly communicating on one side games,…

Optimization and Control · Mathematics 2019-07-03 Tristan Garrec

This paper is concerned with a new type of differential game problems of forwardbackward stochastic systems. There are three distinguishing features: Firstly, our game systems are forward-backward doubly stochastic differential equations,…

Optimization and Control · Mathematics 2015-10-09 Eddie C. M. Hui , Hua Xiao

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

Simple stochastic games can be solved by value iteration (VI), which yields a sequence of under-approximations of the value of the game. This sequence is guaranteed to converge to the value only in the limit. Since no stopping criterion is…

Logic in Computer Science · Computer Science 2021-02-02 Edon Kelmendi , Julia Krämer , Jan Kretinsky , Maximilian Weininger

This paper deals with a two-person zero-sum differential game for a dynamical system described by a Caputo fractional differential equation of order $\alpha \in (0, 1)$ and a Bolza cost functional. The differential game is associated to the…

Optimization and Control · Mathematics 2024-04-25 Mikhail I. Gomoyunov

This paper is an attempt to compute the value and saddle points of zero-sum risk-sensitive average stochastic games. For the average games with finite states and actions, we first introduce the so-called irreducibility coefficient and then…

Optimization and Control · Mathematics 2025-05-08 Fang Chen , Xianping Guo , Xin Guo , Junyu Zhang

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

This article is related to risk-sensitive nonzero-sum stochastic differential games in the Markovian framework. This game takes into account the attitudes of the players toward risk and the utility is of exponential form. We show the…

Optimization and Control · Mathematics 2014-12-04 Said Hamadène , Rui Mu