A game version of the Cowan–Zabczyk–Bruss’ problem

The paper deals with the continuous-time two person non-zero sum game extension of the no information secretary problem. The objects appear according to the compound Poisson process and each player can choose only one applicant. If both players would like to select the same one, then the priority is assigned randomly. The aim of the players is to choose the best candidate. A construction of Nash equilibria for such game is presented. The extension of the game with randomized stopping times is taken into account. The Nash values for such extension are obtained. Analysis of the solutions for different priority defining lotteries is given.