The Monty Hall Problem as a Bayesian Game
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...
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| Format: | Article |
| Language: | English |
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MDPI AG
2017-07-01
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| Series: | Games |
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| Online Access: | https://www.mdpi.com/2073-4336/8/3/31 |
| _version_ | 1818700556873498624 |
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| author | Mark Whitmeyer |
| author_facet | Mark Whitmeyer |
| author_sort | Mark Whitmeyer |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-17T15:06:50Z |
| format | Article |
| id | doaj.art-4e5a0adc575842f79713f0395c2df967 |
| institution | Directory Open Access Journal |
| issn | 2073-4336 |
| language | English |
| last_indexed | 2024-12-17T15:06:50Z |
| publishDate | 2017-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Games |
| spelling | doaj.art-4e5a0adc575842f79713f0395c2df9672022-12-21T21:43:47ZengMDPI AGGames2073-43362017-07-01833110.3390/g8030031g8030031The Monty Hall Problem as a Bayesian GameMark Whitmeyer0Department of Economics, University of Texas at Austin, Austin, TX 78712, USAThis 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.https://www.mdpi.com/2073-4336/8/3/31monty hallequiprobability biasgames of incomplete informationbayes nash equilibrium |
| spellingShingle | Mark Whitmeyer The Monty Hall Problem as a Bayesian Game Games monty hall equiprobability bias games of incomplete information bayes nash equilibrium |
| title | The Monty Hall Problem as a Bayesian Game |
| title_full | The Monty Hall Problem as a Bayesian Game |
| title_fullStr | The Monty Hall Problem as a Bayesian Game |
| title_full_unstemmed | The Monty Hall Problem as a Bayesian Game |
| title_short | The Monty Hall Problem as a Bayesian Game |
| title_sort | monty hall problem as a bayesian game |
| topic | monty hall equiprobability bias games of incomplete information bayes nash equilibrium |
| url | https://www.mdpi.com/2073-4336/8/3/31 |
| work_keys_str_mv | AT markwhitmeyer themontyhallproblemasabayesiangame AT markwhitmeyer montyhallproblemasabayesiangame |