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The Monty Hall Problem as a Bayesian Game

Author

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  • Mark Whitmeyer

    (Department of Economics, University of Texas at Austin, Austin, TX 78712, USA)

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.

Suggested Citation

  • Mark Whitmeyer, 2017. "The Monty Hall Problem as a Bayesian Game," Games, MDPI, vol. 8(3), pages 1-21, July.
    • Handle: RePEc:gam:jgames:v:8:y:2017:i:3:p:31-:d:105869
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    References listed on IDEAS

    as
    1. Friedman, Daniel, 1998. "Monty Hall's Three Doors: Construction and Deconstruction of a Choice Anomaly," American Economic Review, American Economic Association, vol. 88(4), pages 933-946, September.
    2. Peter R. Mueser & Donald Granberg, 1999. "The Monty Hall Dilemma Revisited: Understanding the Interaction of Problem Definition and Decision Making," Experimental 9906001, University Library of Munich, Germany.
    3. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, April.
    4. Richard D. Gill, 2011. "The Monty Hall problem is not a probability puzzle (It's a challenge in mathematical modelling)," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 65(1), pages 58-71, February.
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    Cited by:

    1. Philipp E. Otto, 2022. "Monty Hall three door ’anomaly’ revisited: a note on deferment in an extensive form game," Mind & Society: Cognitive Studies in Economics and Social Sciences, Springer;Fondazione Rosselli, vol. 21(1), pages 25-35, June.

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