Preprint Article Version 1 This version not peer reviewed

The Monty Hall Problem as a Bayesian Game

Version 1 : Received: 25 May 2017 / Approved: 25 May 2017 / Online: 25 May 2017 (08:57:06 CEST)

A peer-reviewed article of this Preprint also exists.

Whitmeyer, M. The Monty Hall Problem as a Bayesian Game. Games 2017, 8, 31. Whitmeyer, M. The Monty Hall Problem as a Bayesian Game. Games 2017, 8, 31.

Journal reference: Games 2017, 8, 31
DOI: 10.3390/g8030031


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 where the contestant is indifferent between switching and not switching. This coincides and agrees with the typical responses and explanations by experimental subjects. Finally, we show that our formulation can explain the experimental results in Page (1998) [12]; that more people gradually choose switch as the number of doors in the problem increases.

Subject Areas

Monty Hall; Equiprobability Bias; games of incomplete information; Bayes Nash Equilibrium

Readers' Comments and Ratings (0)

Leave a public comment
Send a private comment to the author(s)
Rate this article
Views 0
Downloads 0
Comments 0
Metrics 0
Leave a public comment

Notify me about updates to this article or when a peer-reviewed version is published.