The Monty Hall Problem as a Bayesian Game

Whitmeyer, Mark

doi:10.3390/g8030031

Cited by 3 publications

(4 citation statements)

References 18 publications

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“…This problem has been a subject of much debate, with many mistakenly believing in the equiprobability of the remaining doors [14]. The fifty-fifty argument is often cited as an example of the equiprobability bias heuristic [15]. However, the probability of winning does not change after the host reveals a goat, and the unchosen and unrevealed doors hold a two-thirds chance of having the car.…”

Section: The Monty Hall Problemmentioning

confidence: 99%

Are Entrepreneurs Probabilists or Possibilists? Observing Opportunity as Possibilities, Probabilistically

Leong

2024

JCBAR

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This paper explores uncertainty, possibility, and entrepreneurial inclination in entrepreneurship. It presents a novel probabilistic lens to comprehend uncertainty and its impact on entrepreneurial theory and practice, highlighted through analysing decision-making behaviour via the Monty Hall problem. The deterministic perspective is called into question when entrepreneurship is depicted as an agent whose outcomes are indeterminate and probabilistically predetermined. Entrepreneurs effectively handle risk and uncertainty, venturing into uncharted territories to attain possible benefits. The research distinguishes between probabilists, who base their decision-making on likelihoods, and possibilists, who investigate the attainable through imaginative potential. This possibilist approach incorporates concepts of contingency and potential, recognising both the potential outcomes and the associated dangers, making a valuable contribution to practical application. Theoretically, this paper contributes to the entrepreneurship literature by offering the Many-Doors model as a tool for understanding the complex interplay between an individual’s inclination towards probability or possibility and their entrepreneurial decisions. This conceptual model functions as a link integrating elements of risk, uncertainty, and strategic choice, thereby broadening the theoretical frameworks used to analyze entrepreneurial behaviour, potentially resulting in a more holistic understanding of entrepreneurial dynamics.

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Section: The Monty Hall Problemmentioning

confidence: 99%

Are Entrepreneurs Probabilists or Possibilists? Observing Opportunity as Possibilities, Probabilistically

Leong

2024

JCBAR

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“…The MHP has spawned a remarkable amount of attention and controversy. The vast literature regarding the MHP spans myriad disciplines from mathematics, statistics, game theory, quantum information theory, psychology, philosophy, ethology (Gill, 2011), education, sports science, medical decisionmaking, animal science (James et al, 2018), and behavioral economics (Whitmeyer, 2017) to sociology and religion (Bennett, 2018). Interest in the MHP has not been restricted to academic researchers; it may also be found in the popular press (e.g., The Economist, 1999;Tierney, 2008), on YouTube, and in the 2008 Columbia Pictures' movie 21.…”

Section: Literature Review In Briefmentioning

confidence: 99%

“…The literature is ripe with modifications to the game itself, and these might be included in the classroom discussion; for example, that the host and player reveal their choices at the same time (Bailey, 2000) or that the player decides to commit before the host opens one of the remaining doors (e.g., Coutinho et al, 2019;Miller & Sanjurjo, 2019). Perhaps the most common variation to the game involves more than three doors (e.g., Bailey, 2000;Chen & Wang, 2020;Chun, 1999;Granberg & Dorr, 1998;Lucas, Rosenhouse, & Schepler, 2009;Whitmeyer, 2017). Appendix 3 suggests ways to add a more-than-three-doors activity to the classroom.…”

Section: Part 5: Modifications and Extensionsmentioning

confidence: 99%

“…Controversies in the research literature regarding proper solutions to the MHP boil down to assumptions made and perspectives taken (e.g., Chun, 1999;Gill, 2011;Morgan et al, 1991), yet this side of the story has played little to no role in the use of the MHP as a pedagogical tool. Is Monty Hall, for example, a random number generator or an antagonist to the contestant (e.g., Chun, 1999;Whitmeyer, 2017)? In our work, students are challenged to list assumptions, articulate situations under which they might not hold, and propose alternative solutions.…”

Section: Introductionmentioning

confidence: 99%

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The Monty Hall problem as a multifaceted experiential learning exercise in quantitative business courses

Côté

Smith

2021

Decision Sci J Innov Edu

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Popular game shows offer educators the opportunity to develop active-learning exercises that provide students with a real-world connection to analytical reasoning and methods. We describe a classroom assignment developed for quantitative business courses based on the Monty Hall Problem (MHP), a probability puzzle with ties to the long-running television game show Let's Make a Deal. Through a holistic view of the MHP, we provide instructors with various avenues to use the MHP as a comprehensive experiential learning exercise with multiple opportunities for individual and class discussions and exercises. Instructors adopting our multifaceted approach to the MHP will expose students to myriad analytical tools including probability, decision trees, and Monte Carlo simulation as well as to cognitive biases that can affect the decision-making process. Among the unique contributions of our work is its focus on the commonly held MHP assumptions. Specifically, we challenge students to articulate conditions inherent to the MHP solution and assess their appropriateness in context. By relaxing one or more of those assumptions, and observing differences in solutions, students become attuned to the importance of knowing and assessing conditions that underlie all quantitative decision-making tools.

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Monty Hall three door ’anomaly’ revisited: a note on deferment in an extensive form game

Otto

2021

Mind Soc

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The Monty Hall game is one of the most discussed decision problems, but where a convincing behavioral explanation of the systematic deviations from probability theory is still lacking. Most people not changing their initial choice, when this is beneficial under information updating, demands further explanation. Not only trust and the incentive of interestingly prolonging the game for the audience can explain this kind of behavior, but the strategic setting can be modeled more sophisticatedly. When aiming to increase the odds of winning, while Monty’s incentives are unknown, then not to switch doors can be considered as the most secure strategy and avoids a sure loss when Monty’s guiding aim is not to give away the prize. Understanding and modeling the Monty Hall game can be regarded as an ideal teaching example for fundamental statistic understandings.

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The Monty Hall Problem as a Bayesian Game

Cited by 3 publications

References 18 publications

Are Entrepreneurs Probabilists or Possibilists? Observing Opportunity as Possibilities, Probabilistically

Are Entrepreneurs Probabilists or Possibilists? Observing Opportunity as Possibilities, Probabilistically

The Monty Hall problem as a multifaceted experiential learning exercise in quantitative business courses

Monty Hall three door ’anomaly’ revisited: a note on deferment in an extensive form game

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