A note on two person full-information best choice problems with imperfect observation

Abstract

The paper deals with the following zero-sum game version of the full-information best choice problem. Two person observe sequentially a known number of iid random variables from a known continuous distribution with the object of choosing the largest. The random variables cannot be perfectly observed. Each time a random variable is sampled the sampler is informed only whether it is greater than or less than some level specified by him. Players can choose at most one observation. After each sampling players take a decision for acceptance or rejection of the observation. If both want to accept the same observation the priority is given to the specified player, say Player 1. The class of adequate strategies and the suitable gain function for the problem is constructed. It is shown that the game has solution in pure strategies. The numerical examples are given. The random number of observations is also investigated.