Sequential games with random priority

The paper deals with a class of two-person zero-sum sequential games related to a partial observation of random variables X1,X2,...,XN by the players. Each player, based on some indirect information, selects a moment t, l≤t≤N. In this way he communicates that he would like to accept an unknown realization xt of Xt. When only one player selects the moment t then he obtains the required realization. If both players select the same moment t, then there is a lottery choosing either Player 1 or Player 2. The player chosen by the lottery obtains the realization xt and the player thus deprived of the acceptance of xt at t<N, may select any later realization. Each player can accept only one realization. Payoff functions of the players depend on the realizations chosen by them. The normal form of the game is constructed and a solution is given with the help of the help of the dynamic programming method. The results are illustrated by examples.