Material Information 
Title: 
Optimal Behavior of Contrite TitforTat 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 ) borndigital ( 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 limitofmeans or discounting approach. TitforTat is given as an example of a Nash equilibrium for the discounting payoff and the limitofmeans payoff in the errorfree case. Toward an analysis of Nash equilibrium strategies under error, a Markov chain Mï¿½ with associated stationary distribution ï¿½ï¿½ is defined over the states of two given finite state transducers, with transition probabilities as a function of the errorrate parameter ï¿½. The longrun behavior of two finite state transducers under infinitesimal error is given by limï¿½0 (ï¿½ï¿½). 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, limitofmeans under infinitesimal error, is defined as a weighted sum over the possible payoffs given by ï¿½ï¿½0. TitforTat is shown to have poor performance under infinitesimal error, as ï¿½ï¿½?0 gives nonzero probability to states producing defection. The selfcorrecting strategy Contrite TitforTat is shown to be an efficient Nash equilibrium for the set of finitestate transducer strategies with payoff given by limitofmeans under infinitesimal error. Specifically, any other finitestate transducer played against Contrite TitforTat either produces a lower payoff for that player or is, against Contrite TitforTat, 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 ONCAMPUS 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 

Material Information 
Title: 
Optimal Behavior of Contrite TitforTat 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 ) borndigital ( 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 limitofmeans or discounting approach. TitforTat is given as an example of a Nash equilibrium for the discounting payoff and the limitofmeans payoff in the errorfree case. Toward an analysis of Nash equilibrium strategies under error, a Markov chain Mï¿½ with associated stationary distribution ï¿½ï¿½ is defined over the states of two given finite state transducers, with transition probabilities as a function of the errorrate parameter ï¿½. The longrun behavior of two finite state transducers under infinitesimal error is given by limï¿½0 (ï¿½ï¿½). 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, limitofmeans under infinitesimal error, is defined as a weighted sum over the possible payoffs given by ï¿½ï¿½0. TitforTat is shown to have poor performance under infinitesimal error, as ï¿½ï¿½?0 gives nonzero probability to states producing defection. The selfcorrecting strategy Contrite TitforTat is shown to be an efficient Nash equilibrium for the set of finitestate transducer strategies with payoff given by limitofmeans under infinitesimal error. Specifically, any other finitestate transducer played against Contrite TitforTat either produces a lower payoff for that player or is, against Contrite TitforTat, 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 ONCAMPUS 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 
