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Optimal Behavior of Contrite Tit-for-Tat Under Infinitesimal Rate of Error

Permanent Link: http://ncf.sobek.ufl.edu/NCFE003315/00001

Material Information

Title: Optimal Behavior of Contrite Tit-for-Tat Under Infinitesimal Rate of Error
Physical Description: Book
Language: English
Creator: Teravainen, Timothy
Publisher: New College of Florida
Place of Publication: Sarasota, Fla.
Creation Date: 2003
Publication Date: 2003

Subjects

Subjects / Keywords: Game Theory
Mathematics
Prisoner's Dilemma
Genre: bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: The repeated play, with possibility of error, of the Prisoner's Dilemma is studied through the pure Nash equilibria for sets of strategies described by finite state transducers. Payoffs for the repeated game are defined by a limit-of-means or discounting approach. Tit-for-Tat is given as an example of a Nash equilibrium for the discounting payoff and the limit-of-means payoff in the error-free case. Toward an analysis of Nash equilibrium strategies under error, a Markov chain M� with associated stationary distribution �� is defined over the states of two given finite state transducers, with transition probabilities as a function of the error-rate parameter �. The long-run behavior of two finite state transducers under infinitesimal error is given by lim�-0 (��). This distribution is analyzed by the method of stochastic stability as given by Peyton Young and applied to a theory of equilibrium selection in convention games. The results of Peyton Young are discussed and sharpened slightly. A new payoff, limit-of-means under infinitesimal error, is defined as a weighted sum over the possible payoffs given by ��-0. Tit-for-Tat is shown to have poor performance under infinitesimal error, as ��?0 gives non-zero probability to states producing defection. The self-correcting strategy Contrite Tit-for-Tat is shown to be an efficient Nash equilibrium for the set of finite-state transducer strategies with payoff given by limit-of-means under infinitesimal error. Specifically, any other finite-state transducer played against Contrite Tit-for-Tat either produces a lower payoff for that player or is, against Contrite Tit-for-Tat, equivalent to it under noise.
Statement of Responsibility: by Timothy Teravainen
Thesis: Thesis (B.A.) -- New College of Florida, 2003
Electronic Access: RESTRICTED TO NCF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE
Bibliography: Includes bibliographical references.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The New College of Florida, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Local: Faculty Sponsor: McDonald, Patrick

Record Information

Source Institution: New College of Florida
Holding Location: New College of Florida
Rights Management: Applicable rights reserved.
Classification: local - S.T. 2003 T3
System ID: NCFE003315:00001

Permanent Link: http://ncf.sobek.ufl.edu/NCFE003315/00001

Material Information

Title: Optimal Behavior of Contrite Tit-for-Tat Under Infinitesimal Rate of Error
Physical Description: Book
Language: English
Creator: Teravainen, Timothy
Publisher: New College of Florida
Place of Publication: Sarasota, Fla.
Creation Date: 2003
Publication Date: 2003

Subjects

Subjects / Keywords: Game Theory
Mathematics
Prisoner's Dilemma
Genre: bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: The repeated play, with possibility of error, of the Prisoner's Dilemma is studied through the pure Nash equilibria for sets of strategies described by finite state transducers. Payoffs for the repeated game are defined by a limit-of-means or discounting approach. Tit-for-Tat is given as an example of a Nash equilibrium for the discounting payoff and the limit-of-means payoff in the error-free case. Toward an analysis of Nash equilibrium strategies under error, a Markov chain M� with associated stationary distribution �� is defined over the states of two given finite state transducers, with transition probabilities as a function of the error-rate parameter �. The long-run behavior of two finite state transducers under infinitesimal error is given by lim�-0 (��). This distribution is analyzed by the method of stochastic stability as given by Peyton Young and applied to a theory of equilibrium selection in convention games. The results of Peyton Young are discussed and sharpened slightly. A new payoff, limit-of-means under infinitesimal error, is defined as a weighted sum over the possible payoffs given by ��-0. Tit-for-Tat is shown to have poor performance under infinitesimal error, as ��?0 gives non-zero probability to states producing defection. The self-correcting strategy Contrite Tit-for-Tat is shown to be an efficient Nash equilibrium for the set of finite-state transducer strategies with payoff given by limit-of-means under infinitesimal error. Specifically, any other finite-state transducer played against Contrite Tit-for-Tat either produces a lower payoff for that player or is, against Contrite Tit-for-Tat, equivalent to it under noise.
Statement of Responsibility: by Timothy Teravainen
Thesis: Thesis (B.A.) -- New College of Florida, 2003
Electronic Access: RESTRICTED TO NCF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE
Bibliography: Includes bibliographical references.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The New College of Florida, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Local: Faculty Sponsor: McDonald, Patrick

Record Information

Source Institution: New College of Florida
Holding Location: New College of Florida
Rights Management: Applicable rights reserved.
Classification: local - S.T. 2003 T3
System ID: NCFE003315:00001

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