The Monty Hall Problem as a Bayesian Game

Mark Whitmeyer
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Mark Whitmeyer: Department of Economics, University of Texas at Austin, Austin, TX 78712, USA

Games, 2017, vol. 8, issue 3, 1-21

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.

Keywords: monty hall; equiprobability bias; games of incomplete information; bayes nash equilibrium (search for similar items in EconPapers)
JEL-codes: C C7 C70 C71 C72 C73 (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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