Related papers: A zero-sum stochastic differential game with impul…
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…
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…
We prove the dynamic programming principe for uniformly nondegenerate stochastic differential games in the framework of time-homogeneous diffusion processes considered up to the first exit time from a domain. The zeroth-order "coefficient"…
We study zero-sum stochastic games between a singular controller and a stopper when the (state-dependent) diffusion matrix of the underlying controlled diffusion process is degenerate. In particular, we show the existence of a value for the…
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…
In this paper we study a two person zero sum stochastic differential game in weak formulation. Unlike standard literature which uses strategy type of controls, the weak formulation allows us to consider the game with control against…
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…
We consider stochastic impulse control problems when the impulses cost functions are arbitrary. We use the dynamic programming principle and viscosity solutions approach to show that the value function is a unique viscosity solution for the…
In this paper, we consider state and control path-dependent stochastic zero-sum differential games, where the dynamics and the running cost include both state and control paths of the players. Using the notion of nonanticipative strategies,…
We consider an optimal stochastic impulse control problem over an infinite time horizon motivated by a model of irreversible investment choices with fixed adjustment costs. By employing techniques of viscosity solutions and relying on…
In this paper, we formulate a two-player zero-sum game under dynamic constraints defined by hybrid dynamical equations. The game consists of a min-max problem involving a cost functional that depends on the actions and resulting solutions…
This paper is concerned with stochastic impulse control problems in which the running cost changes depending on the impulse control. Because of such a dependence, it brings several difficulties when the usual dynamic programming principle…
This paper considers a formulation of a differential game with constrained dynamics, where one player selects the dynamics and the other selects the applicable cost. When the game is considered on a finite time horizon, its value satisfies…
We show that equilibria of a sequential semi-anonymous nonatomic game (SSNG) can be adopted by players in corresponding large but finite dynamic games to achieve near-equilibrium payoffs. Such equilibria in the form of random…
This paper studies an optimal stochastic impulse control problem in a finite horizon with a decision lag, by which we mean that after an impulse is made, a fixed number units of time has to be elapsed before the next impulse is allowed to…
The paper is concerned with a zero-sum continuous-time stochastic differential game with a dynamics controlled by a Markov process and a terminal payoff. The value function of the original game is estimated using the value function of a…
We consider a two-player zero-sum stochastic differential game in which one of the players has a private information on the game. Both players observe each other, so that the non-informed player can try to guess his missing information. Our…
We consider discrete time partially observable zero-sum stochastic game with average payoff criterion. We study the game using an equivalent completely observable game. We show that the game has a value and also we come up with a pair of…
We prove that zero-sum Dynkin games in continuous time with partial and asymmetric information admit a value in randomised stopping times when the stopping payoffs of the players are general \cadlag measurable processes. As a by-product of…
In stochastic games with stage duration h, players act at times 0, h, 2h, and so on. The payoff and leaving probabilities are proportional to h. As h approaches 0, such discrete-time games approximate games played in continuous time. The…