The TwoEnvelope Problem: A Numerical Simulation
(2021) In Bachelor's Theses in Mathematical Sciences MASK11 20201Mathematical Statistics
 Abstract
 We study a version of the twoenvelope 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 twoenvelope game were performed for a sample continuous and a sample discrete distribution. The... (More)
 We study a version of the twoenvelope 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 twoenvelope game were performed for a sample continuous and a sample discrete distribution. The switching strategy’s cumulative and average winnings exceed the nonswitching 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/studentpapers/record/9041156
 author
 Abdallah, Kawthar ^{LU}
 supervisor

 Magnus Wiktorsson ^{LU}
 organization
 course
 MASK11 20201
 year
 2021
 type
 M2  Bachelor Degree
 subject
 publication/series
 Bachelor's Theses in Mathematical Sciences
 report number
 LUNFMS40512021
 ISSN
 16546229
 other publication id
 2021:K8
 language
 English
 id
 9041156
 date added to LUP
 20210415 15:06:52
 date last changed
 20210603 15:31:47
@misc{9041156, abstract = {{We study a version of the twoenvelope 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 twoenvelope game were performed for a sample continuous and a sample discrete distribution. The switching strategy’s cumulative and average winnings exceed the nonswitching 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 = {{16546229}}, language = {{eng}}, note = {{Student Paper}}, series = {{Bachelor's Theses in Mathematical Sciences}}, title = {{The TwoEnvelope Problem: A Numerical Simulation}}, year = {{2021}}, }