To Switch or Not To Switch?

by Kam Hon Chu.

Abstract: This note shows that when the Bayes formula and certain game theory concepts are appropriately applied, the posterior probability of winning a prize in the famous Monty Hall game is not the counter-intuitive answer of 2/3 but it is 1/2. The moral of this exercise is that the Bayes formula should not be applied mechanically. Its application is both art and science. As in the case of equilibrium refinements in game theory, application of the Bayes formula requires both working backward and forward through the game tree.

Key Words: Bayes Theorem, Dynamic Game with Asymmetric Information, Monty Hall Problem, Statistical Decision Theory

Author:
Kam Hon Chu, kchu@mun.ca

Editor: Dean Foster,foster@compstat.wharton.upenn.edu

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