On the Information Economics Approach to the Generalized Game Show Problem

Abstract

The game show problem has received considerable attention since it appeared in Marilyn vos Savant's column in the Parade Magazine. I consider in this article the player's optimal decision strategy and the probability of winning the prize in a generalized version of the game show problem. By means of the information economics approach, we can easily (1) represent the host's various strategies as a simple matrix form; (2) extend the problem to more-than-three-door cases; (3) incorporate the player's prior information; and (4) consider the problem in which the player's choice behavior depends not on the probability of winning the prize, but on the expected utility in the generalized game show problem. The intricacies of this wonderfully confusing little problem make it an excellent tool in teaching probability and statistics courses.

Key Words:

• Bayes rule
• Decision analysis
• Information economics
• Probability models