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The Two-Envelope Problem: A Numerical Simulation

Abdallah, Kawthar LU (2021) In Bachelor's Theses in Mathematical Sciences MASK11 20201
Mathematical 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:
author
Abdallah, Kawthar LU
supervisor
organization
course
MASK11 20201
year
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
2021-06-03 15:31:47
@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}},
}