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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.
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 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.
Keywords
Monty Hall; Equiprobability Bias; games of incomplete information; Bayes Nash Equilibrium
Subject
Business, Economics and Management, Economics
Copyright: 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.
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