Soft estimates of the ability level of a testee

A mathematical model for pedagogical measurements is considered. In the model the decision functions of a testee are the functions of his test score. The calculation of the ability level of a testee and the difficulty level of test items are performed in the framework of the item response theory using the Rasch model. For the mathematical model of decision making we consider a statistical game of a testee against the examiner. In depending on the type of the pay-off function of the game we find confidence intervals for the ability level of a testee or the type of the University where the testee could be learn. The approach proposed enables one to calculate the accuracy and reliability of the decisions. In the game the testee optimal strategies are the randomized decision functions that depend on the test score.