Games 2017, 8(3), 31; doi:10.3390/g8030031
The Monty Hall Problem as a Bayesian Game
Department of Economics, University of Texas at Austin, Austin, TX 78712, USA
Received: 25 May 2017 / Revised: 7 July 2017 / Accepted: 20 July 2017 / Published: 26 July 2017
Abstract
This paper formulates the classic Monty Hall problem as a Bayesian game. Allowing Monty a small amount of freedom in his decisions facilitates a variety of solutions. The solution concept used is the Bayes Nash Equilibrium (BNE), and the set of BNE relies on Monty’s motives and incentives. We endow Monty and the contestant with common prior probabilities (p) about the motives of Monty and show that, under certain conditions on p, the unique equilibrium is one in which the contestant is indifferent between switching and not switching. This coincides and agrees with the typical responses and explanations by experimental subjects. In particular, we show that our formulation can explain the experimental results in Page (1998), that more people gradually choose switch as the number of doors in the problem increases. View Full-Text
Figure 1
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
Share & Cite This Article
MDPI and ACS Style
Whitmeyer, M. The Monty Hall Problem as a Bayesian Game. Games 2017, 8, 31.
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.