Random Priority Two-Person Full Information Best-Choice Game with Disorder

The following version of the two player full information best-choice game is considered. Two players observe the sequence of independent identical distributed random variables with the object of choosing the largest. The distribution law of observations changes at the random moment. A random assignment mechanism is used to give an observation to one of the players. Each of the players can choose at most one observation. The class of adequate strategies and the suitable gain function for the problem is constructed. A numerical examples are given.