In 2012, the scientific world has lost N.N. Krasovskii, an extraordinary mathematician and mechanician whose works have prominently influenced a number of mathematic fields: differential equations, optimal control, and dynamic games theory. His research had profound effects on the development of...

This paper studies a transboundary pollution problem between two neighbour regions as a dynamic game. These two regions do not only share an environmental problem but they are also engaged in interregional trade. A good produced in one region is traded to the other which uses it as an input....

In this paper, a linear dynamical system controlled under the conditions of disturbances and with control delays is considered. The Euclidean norm of a set of the system motion deviations at given instants of time from given targets is minimized. Within the game-theoretical approach the problem...

The model proposed in this paper investigates a differential Cournot oligopoly game with nonrenewable resource exploitation, in which each firm may exploit either its own private pool or a common pool jointly with the rivals. Firms use a deterministic technology to invest in exploration...

This paper deals with the issue of shelf-space allocation and advertising decisions in marketing channels. We consider a network composed of a unique retailer offering the products of two competing manufacturers. The retailer controls the amount of shelf-space to allocate to both brands, while...

We investigate an impulse control differential game arising in a problem of option pricing in mathematical finance. In a previous paper, it was shown that its Value function in ℝ3 could be described as a pair of functions affine in one of the variables, joined on a 2D manifold. Depending on...

We study a zero-sum differential game where the players have only an unperfect information on the state of the system. In the beginning of the game only a random distribution on the initial state is available. The main result of the paper is the existence of the value obtained through an...

The literature on advertising and promotions can be divided in two categories. A first group of models assume that promotion contributes (positively) to the goodwill towards the product, and a second group assumes that promotions reduce that goodwill. In this paper we build a differential game...

Examples with zero-sum linear differential games of fixed terminal time and a convex terminal payoff function depending on two components of the phase vector are considered. Such games can have an indifferent zone with constant value function. The level set of the value function associated with...

In this paper the problem of allocation over time of total cost incurred by coalitions of countries in a coalitional game of pollution reduction is considered. The Nash equilibrium in the game played by coalitions is computed and then the value of each coalition is allocated according to some...