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Strategic Interaction in the Prisoner's STRATEGIC INTERACTION IN THE PRISONER’S DILEMMA: A GAME-THEDREHC DIMENSION OF CONFLICT RESEARCH submitted by Louis Joshua Marinoff for the Degree of Ph.D. in the Philosophy of Science at University College London ProQuest Number: 10609101 All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted. In the unlikely event that the author did not send a com plete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion. uest ProQuest 10609101 Published by ProQuest LLC(2017). Copyright of the Dissertation is held by the Author. All rights reserved. This work is protected against unauthorized copying under Title 17, United States C ode Microform Edition © ProQuest LLC. ProQuest LLC. 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, Ml 48106- 1346 2 ABSTRACT This four-part enquiry treats selected theoretical and empiri­ cal developments in the Prisoner's Dilemma. The enquiry is oriented within the sphere of game-theoretic conflict research, and addresses methodological and philosophical problems embedded in the model under consideration. In Part One, relevant taxonomic criteria of the von Neumann^ Morgenstem theory of games are reviewed, and controversies associ­ ated with both the utility function and game-theoretic rationality are introduced. In Part Two, salient contributions by Rapoport and others to the Prisoner's Dilemma are enlisted to illustrate the model's conceptual richness and problematic wealth. Conflicting principles of choice, divergent concepts of rational choice, and attempted resolutions of the dilemma are evaluated in the static mode. In Part Three, empirical interaction among strategies is examined in the iterated mode. A computer-simulated tournament of competing families of strategies is conducted, as both a complement to and continuation of Axelrod's previous tournaments. Combinatoric sub-tournaments are exhaustively analyzed, and an eliminatory ecolog­ ical scenario is generated. In Part Four, the performance of the maximization family of strategies is subjected to deeper analysis, which reveals critical strengths and weaknesses latent in its dec­ ision-making process. On the whole, an inter-modal continuity obtains, which suggests that the maximization of expected utility, weighted toward probabil­ istic co-operation, is a relatively effective strategic embodiment of Rapoport's ethic of collective rationality. 3 TABLE OF CONTENTS List of Games, Graphs, Tables, and Sample P r o g r a m s ........... 4 Introduction .............................................. 9 Part One: Game-Theoretic Background........................ 12 Chapter I - Taxonomic C r i t e r i a ................. 13 Chapter II - The Utility R m c t i o n ................ 25 Chapter III - Game-Theoretic Ra t i o n a l i t y........ 44 Part Two: The Static Prisoner's Dilemma............... 58 Chapter IV - Conflicting Choices and Rationalities . 59 Chapter V - A Resolution Via Newcomb's P a r a d o x .. 76 Chapter VI - A Meta-Game Resolution.............. 93 Part Three: The Iterated Prisoner's Pi le m m a ................. 104 Chapter VII - A Tournament of Strategic Families .... 105 Chapter VIII - Analysis of Sub-Tournaments...... 131 Chapter IX - An Ecological Scenario.............. 153 Part Four: The Ethic of Collective R a t i o n a l i t y............. 185 Chapter X - The Maximization Family Versus Others .... 186 Chapter XI - The Maximization Family Versus Itself . 204 Chapter XII - Summary and Conclusions............ 231 A p p e n d i c e s .............................................. 257 Appendix I - Glossary of Strategies ................ 258 Appendix II - Table of Raw Scores .................. 261 Appendix III - Efficiency T a b l e s .................... 262 Appendix IV - Sample Programs........................ 271 References 291 4 LIST OF GAMES, GRAPHS, TARI.FS, AND SAMPLE PROGRAMS Games: Game 1.1 - Generalized Matrix of C h o i c e s .................. 18 Game 1.2 - Generalized Matrix of Utilities ................. 19 Game 1.3 - A Case in V/hich All Operators C o m m u t e ........... 19 Game 1.4 - A Case in Which Not All Operators Co m m u t e ........ 20 Game 1.5 - A Saddle P o i n t ................................. 22 Game 1.6 - No Saddle P o i n t ............................... 22 Game 2.1 - A Constant-Sum G a m e ............................ 28 Game 2.2 - A Zero-Sum G a m e ............................... 28 Game 2.3 - Rock, Scissors, P a p e r .......................... 36 Game 2.4 - Weighted Probability Matrix for Rock, Scissors, P a p e r .......................... 38 Game 2.5 - Re-Weighted Probability Matrix for Rock, Scissors, P a p e r .......................... 39 Game 2.6 - Matching Pennies............................... 41 Game 2.7 - Probability Matrix for Matching P e n n i e s ......... 41 Game 2.8 - Fallacious Relative Frequency M a t r i x ............. 42 Game 3.1 - Observer's Meta-Matrix for Player A ............. 51 Game 3.2 - Observer's Meta-Matrix for Player A ............. 53 Game 3.3 - Pascal's Question .............................. 55 Game 4.1 - The Prisoner's Dilemma.......................... 61 Game 4.2 - Strong Dominance............................... 63 Game 4.3 - Weak Dominance................................. 63 Game 4.4 - The Prisoner's Non-Dilemma...................... 70 Game 5.1 - Newcomb's P a r a d o x .............................. 77 Game 5.2 - Being's View ................................. 82 Game 5.3 - Being's Alternative View .................... 82 Game 5.4 - Newcomb's Paradox Reformulated.... ............... 84 Game 5.5 - Prisoner's Dilemma Reformulated................. 86 Game 5.6 - Newcomb's Paradox, Levi's Case 1 ................. 87 Game 5.7 - Newcomb's Paradox, Levi's Case 2 ................. 89 Game 5.8 - Newcomb's Paradox, Levi's Case 3 ................. 89 Game 6.1 - Prisoner's D ilemma.............................. 95 Game 6.2 - First-Level Meta-Game of Game 6 . 1 ............... 95 Game 6.3 - Sub-Matrix of Game 6 . 2 .......................... 96 Game 6.4 - Second-Level Meta-Game of Game 6 . 1 ............... 97 Game 6.5 - Sub-Matrix of Game 6 . 4 .......................... 100 5 Game 7.1 - The Iterated Prisoner's D i l e m m a ................. 109 Game 7.2 - Axelrod's Tournament M a t r i x .................... 109 Game 7.3 - Event Matrix, Maximization Strategy vs Opponent . 119 Game 7.4 - MEU versus TOC, Event Matrix After 100 Moves .... 121 Game 7.5 - MAD versus TOC, Event Matrix After 100 Moves .... 122 Game 7.6 - MAE versus TOC, Event Matrix After 100 Moves .... 123 Game 7 . 7 - MAC versus TOC, Event Matrix After 100 Moves .... 124 Game 9.1 - The Maynard Smith Evolutionary M o d e l ............. 154 Game 9.2 - Encounters Between Pure Strategies............... 155 Game 9.3 - The Prisoner's Dilemma.......................... 158 Game 10.1 - MAD versusCCC, Event Matrix After 100 Moves . .. 188 Game 10.2 - MAD versus CCC, Event Matrix After 200 Moves . .. 188 Game 10.3 - MAD versus CCC, Event Matrix After 1000 Moves . 189 Game 10.4 - MEU versus CCC, Event Matrices (100 & 1000 Moves). 189 Game 10.5 - MAE versus CCC, Event Matrices (100 & 1000 Moves) . 190 Game 10.6 - MAC versus CCC, Event Matrices (100 & 1000 Moves). 190 Game 10.7 - MAD versus TFT, Event Matrices (100 & 1000 Moves) . 191 Game 10.8 - MEU versus TFT, Event Matrices (100 & 200 Moves) . 193 Game 10.9 - MEU versus TFT, Event Matrices (400 & 500 Moves) . 194 Game 10.10 - MEU versus TFT, Event Matrices (900 &. 1000 Moves) 195 Game 10.11 - MAE versus TFT, Event Matrices (100 & 200 Moves) . 196 Game 10.12 - MAE versus TFT, Event Matrices (900 & 1000 Moves) 196 Game 10.13 - MAC versus TFT, Event Matrices (100 & 200 Moves) . 197 Game 10.14 - MAC versus TFT, Event Matrix After 1000 Moves . 199 Game 11.1 - Probability Matrix for RAN versus TOC ............ 205 Game 11.2 - Most Probable Event Matrix for MAD versus MAD (100 M o v e s ) .................... 209 Game 11.3 - Most Probable Event Matrix for MEU versus MEU (100 M o v e s ) .................... 210 Game 11.4 - Most Probable Event Matrix for MAE versus MAE (100 Moves) .................... 211 Game 11.5 - Most Probable Event Matrix for MAC versus MAC (100 Moves) .................... 213 Game 11.6 - Most Probable Event Matrix for MAX versus MAX (100 M o v e s ) .................... 215 Game 11.7 - MAX versus MAX (p=37/100), Initial & Final Event M a t r i c e s ................. 216 Game 11.8 - MAX versus MAX (p=36/100). Initial & Final Event M a t r i c e s ................. 217 Game 11.9 - MAX versus MAX (p=99/100). Initial & Final Event M a t r i c e s ................. 217 Game 12.1 - MAX versus GPP, Consecutive Event Matrices .... 251 Game 12.2 - MAX versus CPP, Consecutive Event Matrices .... 252 6 Graphs: Graph 4.1 - Regions of Co-operation and Defection............ 67 Graph 8.1- Most Efficient Combinatoric Performances........ 151 Graph 9.1 - Ecology of Main Tournament (Initial vs. Stable States) .................... 164 Graph 9.2 - Rates of Population Change (Most Fecund Strategies) ...................... 166 Graph 9.3 - Ecology of Nineteen Survivors (Initial vs. Stable States).................... 167 Graph 10.1 - Maximization Family versus TFT ................. 199 Graph 11.1 - RAN versus TQC, Histogram of RAN1 s Scores for 100 G a m e s .................... 206 Graph 11.2 - TQC versus RAN, Histogram of TQC's Scores for 100 G a m e s .................... 206 Graph 11.3 - EEE versus ETH, Histogram of BEE s Scores for 100 G a m e s .................... 207 Graph 11.4 - ETH versus EEE, Histogram of E T H s Scores for 100 G a m e s .................... 207 Graph 11.5 - CHA versus MAE, Histogram of CHA's Scores for 100 G a m e s .................... 208 Graph 11.6 - MAD versus MAD, Histogram of Scores for 100 G a m e s .........................
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