NON-ZERO-SUM BEST-CHOICE GAMES WHERE TWO STOPS ARE REQUIRED

摘要

Suppose that players Ⅰ and Ⅱ want to jointly employ two secretaries successively one-by-one from a set of n applicants. Best ability of management (foreign language) is wanted by Ⅰ (Ⅱ). We assume that these two kinds of abilities are mutually independent for every applicant. Applicants present themselves one-by-one sequentially. Facing each applicant, each player chooses either to Accept or to Reject. The game ends either when the second time of choice-pair A-A happens getting the payoffs predetermined by the game rule, or when n - 2 applicants except the last two are rejected. If choice-pair is A-R or R-A, then arbitration comes in and forces players to take the same choice as I's (II's) with probability p (p), 1/2 ≤ p ≤ 1. Each player aims to maximize the expected payoff he can get. Explicit solutions are derived to this n-stage game, for the cases where abilities of each applicant are observed as bivariate random variables with full-information and with no-information. Some numerical results are presented.