Related papers: On a Stopping Game in continuous time

Games, in their mathematical sense, are everywhere (game industries, economics, defense, education, chemistry, biology, ...).Search algorithms in games are artificial intelligence methods for playing such games. Unfortunately, there is no…

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…

We study a game where one player selects a random function, and the other has to guess that function, and show that with high probability the second player can correctly guess most of the random function. We apply this analysis to…

This paper is concerned with the controller-and-stopper stochastic differential game under a regime switching model in an infinite horizon. The state of the system consists of a number of diffusions \emph{coupled} by a continuous-time…

We study a class of two-player zero-sum stochastic games known as \textit{blind stochastic games}, where players neither observe the state nor receive any information about it during the game. A central concept for analyzing long-duration…

We investigate a two-player zero-sum stochastic differential game in which one of the players has more information on the game than his opponent. We show how to construct numerical schemes for the value function of this game, which is given…

We introduce an efficient numerical scheme for continuous time Dynkin games under model uncertainty. We use the Skorokhod embedding in order to construct recombining tree approximations. This technique allows us to determine convergence…

In this paper, we consider a zero-sum undiscounted stochastic game which has finite state space and finitely many pure actions. Also, we assume the transition probability of the undiscounted stochastic game is controlled by one player and…

We investigate how well continuous-time fictitious play in two-player games performs in terms of average payoff, particularly compared to Nash equilibrium payoff. We show that in many games, fictitious play outperforms Nash equilibrium on…

Shapley's discounted stochastic games, Everett's recursive games and Gillette's undiscounted stochastic games are classical models of game theory describing two-player zero-sum games of potentially infinite duration. We describe algorithms…

A Dynkin game is considered for stochastic differential equations with random coefficients. We first apply Qiu and Tang's maximum principle for backward stochastic partial differential equations to generalize Krylov estimate for the…

We consider a stochastic differential game in the context of forward-backward stochastic differential equations, where one player implements an impulse control while the opponent controls the system continuously. Utilizing the notion of…

We develop a theory for solving continuous time optimal stopping problems for non-linear expectations. Our motivation is to consider problems in which the stopper uses risk measures to evaluate future rewards.

In the present paper we consider one class of zero-sum games with discontinuous payoffs which may have no solutions in the sets of pure or mixed strategies. We show that, however, the solution always exists in the set of so-called $\mathcal…

In this paper we investigate a differential game in which countably many dynamical objects pursue a single one. All the players perform simple motions. The duration of the game is fixed. The controls of a group of pursuers are subject to…

We explore properties of the value function and existence of optimal stopping times for functionals with discontinuities related to the boundary of an open (possibly unbounded) set $\mathcal{O}$. The stopping horizon is either random, equal…

Using methods from the statistical mechanics of disordered systems we analyze the properties of bimatrix games with random payoffs in the limit where the number of pure strategies of each player tends to infinity. We analytically calculate…

We consider the behaviour of $\lambda$-discounted zero-sum games as the discount factor $\lambda$ approaches 0 (that is, the players are more and more patient), in the context of games with stage duration. In stochastic games with stage…

We consider the mean-field game where each agent determines the optimal time to exit the game by solving an optimal stopping problem with reward function depending on the density of the state processes of agents still present in the game.…

This paper considers the problem of two-player zero-sum stochastic differential game with both players adopting impulse controls in finite horizon under rather weak assumptions on the cost functions ($c$ and $\chi$ not decreasing in time).…