In this paper the set of value functions of all-possible zero-sum differential games with terminal payoff is characterized. The necessary and sufficient condition for a given function to be a value of some differential game with terminal payoff is obtained.

In this paper we use techniques of Malliavin calculus and forward integration to present a general stochastic maximum principle for anticipating stochastic differential equations driven by a Lévy type of noise. We apply our result to study a general stochastic differential game problem of an insider. MSC2010 : 60G51, 60H40, 60H10, 60HXX, 93E20

To find the possible equilibrium states of forest ecosystems one are suggested to use the theory of differential games. At within the 4-tier model of mosaic forest communities it established the existence of the Nash equilibrium states in such ecosystems. Key–Words: Forest ecosystem, the equilibrium of the ecosystem, differential game, Nash equilibrium October 30, 2016

Berkovitz’s notion of strategy and payoff for differential games is extended to study two player zero-sum infinite dimensional differential games on the infinite horizon with discounted payoff. After proving dynamic programming inequalities in this framework, we establish the existence and characterization of value. We also construct a saddle point for the game. Mathematical subject classificat...

The authors of this talk work at the Institute of Mathematics and Mechanics in Ekaterinburg, Russia. The basic subject of their scientific investigations is differential game theory. Sergey Kumkov has a one-semester course on optimal control at the Physics Department of Urals University. Valerii Patsko reads a one-semester course on optimal control and differential games at the Mathematical Dep...

1. Introduction. Two person zero-sum differential games can be considered as control problems with two opposing controllers or players. One player seeks to maximize and one to minimize the pay-off function. The greatest pay-off that the maximizing player can force is termed the lower value of the game and similarly the least value which the minimizing player can force is called the upper value....

This paper studies the mixed zero-sum stochastic differential game problem. We allow functionals and dynamics to be of polynomial growth. The problem is formulated as an extended doubly reflected BSDEs with a specific generator. show existence solution for this we prove saddle-point game. Moreover, in Markovian framework that value function unique viscosity associated Hamilton–Jacobi–Bellman (H...

Consider a market in which firms accumulate capital according to the Nerlove-Arrow capital accumulation equation. Each player chooses a path of investment and thus an induced path of capital to maximize his total discounted profits which depend on his own capital and the capital stocks of his rivals. Existence is proved for such a nonzero sum, infinite horizon differential game and conditions u...

We consider a zero-sum stochastic differential controller-and-stopper game in which the state process is a controlled diffusion evolving in a multi-dimensional Euclidean space. In this game, the controller affects both the drift and the volatility terms of the state process. Under appropriate conditions, we show that the game has a value and the value function is the unique viscosity solution t...