The Two-Envelope Problem: A Numerical Simulation
(2021) In Bachelor's Theses in Mathematical Sciences MASK11 20201Mathematical Statistics
- Abstract
- We study a version of the two-envelope problem where a host presents two indistinguishable envelopes to a player. a player is informed that the monetary content of one of the envelopes is twice that of the other and is then allocated one of the envelopes. The player decides whether or not to keep the allocated envelope knowing the content of the allocated envelope and the probability distribution of how the lower value of the envelopes is generated. We obtains conditions for switching envelopes for continuous and discrete distributions and show optimality for each strategy’s expected benefit. Numerical simulations for 10,000 instances of the two-envelope game were performed for a sample continuous and a sample discrete distribution. The... (More)
- We study a version of the two-envelope problem where a host presents two indistinguishable envelopes to a player. a player is informed that the monetary content of one of the envelopes is twice that of the other and is then allocated one of the envelopes. The player decides whether or not to keep the allocated envelope knowing the content of the allocated envelope and the probability distribution of how the lower value of the envelopes is generated. We obtains conditions for switching envelopes for continuous and discrete distributions and show optimality for each strategy’s expected benefit. Numerical simulations for 10,000 instances of the two-envelope game were performed for a sample continuous and a sample discrete distribution. The switching strategy’s cumulative and average winnings exceed the non-switching strategy’s winnings in both scenarios.In both the discrete and continuous cases, knowing the distribution of the initial amount and the allocated amount leads to the optimal strategy for switching envelopes. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/student-papers/record/9041156
- author
- Abdallah, Kawthar LU
- supervisor
- organization
- course
- MASK11 20201
- year
- 2021
- type
- M2 - Bachelor Degree
- subject
- publication/series
- Bachelor's Theses in Mathematical Sciences
- report number
- LUNFMS-4051-2021
- ISSN
- 1654-6229
- other publication id
- 2021:K8
- language
- English
- id
- 9041156
- date added to LUP
- 2021-04-15 15:06:52
- date last changed
- 2024-02-16 17:17:41
@misc{9041156, abstract = {{We study a version of the two-envelope problem where a host presents two indistinguishable envelopes to a player. a player is informed that the monetary content of one of the envelopes is twice that of the other and is then allocated one of the envelopes. The player decides whether or not to keep the allocated envelope knowing the content of the allocated envelope and the probability distribution of how the lower value of the envelopes is generated. We obtains conditions for switching envelopes for continuous and discrete distributions and show optimality for each strategy’s expected benefit. Numerical simulations for 10,000 instances of the two-envelope game were performed for a sample continuous and a sample discrete distribution. The switching strategy’s cumulative and average winnings exceed the non-switching strategy’s winnings in both scenarios.In both the discrete and continuous cases, knowing the distribution of the initial amount and the allocated amount leads to the optimal strategy for switching envelopes.}}, author = {{Abdallah, Kawthar}}, issn = {{1654-6229}}, language = {{eng}}, note = {{Student Paper}}, series = {{Bachelor's Theses in Mathematical Sciences}}, title = {{The Two-Envelope Problem: A Numerical Simulation}}, year = {{2021}}, }