Related papers: Explicit solution to an optimal two-player switchi…

We study stochastic two-player turn-based games in which the objective of one player is to ensure several infinite-horizon total reward objectives, while the other player attempts to spoil at least one of the objectives. The games have…

In this paper, a large class of time-varying Riccati equations arising in stochastic dynamic games is considered. The problem of the existence and uniqueness of some globally defined solution, namely the bounded and stabilizing solution, is…

We study a class of second order variational inequalities with bilateral constraints. Under certain conditions we show the existence of a unique viscosity solution of these variational inequalities and give a stochastic representation to…

We consider a robust switching control problem. The controller only observes the evolution of the state process, and thus uses feedback (closed-loop) switching strategies, a non standard class of switching controls introduced in this paper.…

Two-player graph games have found numerous applications, most notably in the synthesis of reactive systems from temporal specifications, but also in verification. The relevance of infinite-state systems in these areas has lead to…

Reach-avoid differential games play an important role in collision avoidance, motion planning and control of aircrafts, and related applications. The central problem is the computation of the set of initial states from which the ego player…

This paper provides sufficient conditions for the existence of solutions for two-person zero-sum games with inf/sup-compact payoff functions and with possibly noncompact decision sets for both players. Payoff functions may be unbounded, and…

Pursuit-evasion scenarios appear widely in robotics, security domains, and many other real-world situations. We focus on two-player pursuit-evasion games with concurrent moves, infinite horizon, and discounted rewards. We assume that the…

This paper studies a class of zero-sum stopping game in a regime switching model. A verification theorem as a sufficient criterion for Nash equilibriums is established based on a set of variational inequalities (VIs). Under an appropriate…

We introduce two-level discounted games played by two players on a perfect-information stochastic game graph. The upper level game is a discounted game and the lower level game is an undiscounted reachability game. Two-level games model…

In this paper we find viscosity solutions to a coupled system composed by two equations, the first one is parabolic and driven by the infinity Laplacian while the second one is elliptic and involves the usual Laplacian. We prove that there…

Infinite horizon optimal stopping problems for a L\'evy processes with a two-sided reward function are considered. A two-sided verification theorem is presented in terms of the overall supremum and the overall infimum of the process. A…

In the paper it is proven that the two-players turn-based stochastic game "Risk or Safety" has a unique solution. Both players need to play the same strategy if they want to maximize their winning chances. An analytical method based on the…

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…

In this paper, we study a game with positive or plus infinite expectation and determine the optimal proportion of investment for maximizing the limit expectation of growth rate per attempt. With this objective, we introduce a new pricing…

We study the ergodicity of deterministic two-person zero-sum differential games. This property is defined by the uniform convergence to a constant of either the infinite-horizon discounted value as the discount factor tends to zero, or…

We address the problem of making a managerial decision when the investment project is subsidized, which results in the resolution of an infinite-horizon optimal stopping problem of a switching diffusion driven by either an homogeneous or an…

In this paper, we undertake an investigation into the utility maximization problem faced by an economic agent who possesses the option to switch jobs, within a scenario featuring the presence of a mandatory retirement date. The agent needs…

We are interested in the convergence of the value of n-stage games as n goes to infinity and the existence of the uniform value in stochastic games with a general set of states and finite sets of actions where the transition is commutative.…

In this paper, we study systems of nonlinear second-order variational inequalities with interconnected bilateral obstacles with non-local terms. They are of min-max and max-min types and related to a multiple modes zero-sum switching game…