Stochastic Game with Lexicographic Payoffs

Stochastic games are discussed as a priva-te class of a general dynamic games. A certain class of lexicographic noncooperative games is studied lexicographic stochastic matrix games ) ,..., ( 1 m . The problem of the existence of Nash equilibrium is studied with two analyses standard and nonstandard way. Standard means using the same kind of mixed strategies in case of scalar games. In this case in lexicographic stochastic matrix game Nash equilibrium may not be existed. Its existence takes place in relevant stochastic affine matrix game to the existence of Nash equilibrium. In L game a set of Nash equi-librium is given by means of relevant stochastic affine matrix game's set of equilibrium. The sufficient condi-tions of the existance such affine game is proved. In nonstandard way of analyses we use such mixed stra-tegies, they use m ,..., 1 components with lexicog-raphic probabilites. In this case the kinds of subsets of a set of equilibrium in L game are described.