ИСТИНА

The results of the joint work with Marianne Akian and Stephane Gaubert will be presented. Tropical algebra (sometimes called max algebra) is a set of real numbers equipped with the maximum operation instead of usual addition and addition instead of usual multiplication. Under these operations this is an algebraic structure called a semiring. Such structures naturally appear in modern scheduling theory, control theory, optimization, dynamical systems and networks. Tropical arithmetic allows to reduce difficult non-linear problems to the linear problems but over tropical semiring. Therefore, to investigate these problems it is necessary to develop linear algebra in the tropical case. This subject is very actual nowdays. We plan to introduce and investigate tropical linear algebra and to connect it with the game theory. In particular, we will present our recent results on the relationships between the emptyness of tropical polyhedra and the existence of the winning strategy in two player mean pay off game and other related results.