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Thucydides “The Father of Game Theory” in a Paper Called Thucydides on Nash Versus Stackelberg: the Importance of the Sequence of Moves in Games.8

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THUCYDIDES: FATHER OF GAME THEORY Maria Manuela Wagner Dal Borgo Department of Greek and Latin University College London This thesis is submitted in fulfilment of the requirements for the degree of Doctor of Philosophy July 2015 1 Declaration ‘I, Maria Manuela Wagner Dal Borgo, confirm that the work presented in this thesis is my own. Where information has been derived from other sources, I confirm that this has been indicated in the thesis.’ Signed: Maria Manuela Wagner Dal Borgo Date: 31.07.2015 2 Abstract Thesis Title: THUCYDIDES: FATHER OF GAME THEORY In this thesis, I interpret Thucydides’ History of the Peloponnesian War utilizing models of game theory to distil the abstract strategic structures that Thucydides illuminates. It is possible by close analysis of the narrative to extract an implicit descriptive theory embedded in the narrative, never made explicit but a consistent presence wherever characters, groups and nations interact. Game theory in its informal structure (i.e. without deploying the full formal apparatus of mathematics) offers a valuable extension to narratology, a narrative theory already successfully introduced into Classical studies. The thesis studies Thucydides’ conception of the agon (contest/competition) in its basic framework from simple strategic and dynamic games to games with boundedly rational players. I argue that Thucydides describes a tropology of interaction by inferring motivations from observed actions. Chapter 1 and 2 discuss Thucydides’ method of reading the minds of historical agents to explore historical causation in simultaneous move and sequential move environments, respectively. Chapter 3 discusses agents with incomplete information and also agents who take irrational decisions. Thucydides allows room in his narrative for players to miscalculate or make conjectures when faced with an interactive environment. He writes history as a description of similar types of potentially recurrent events and sequences linked by a causal chain, whose outcomes are only probabilistically predictable. Whilst analysing different types of interactions, the study aims to explore different game theoretic models based on Thucydides’ tropology of interaction, in order to identify in the final chapter new research directions for rational actor models as well as stochastic environments for the benefit of political science. 3 Table of Contents Declaration 2 Abstract 3 Table of Contents 4 List of Tables and Images 7 Abreviations 8 Introduction 10 Methodology 15 Thucydides’ Method for Modern theorists 16 Thucydides, Game theory and Narratology 19 Game Theory retells the Story 26 Players, Actions, Preferences and Outcomes 27 Basic Types of Games 30 The first Thucydidean game theorist 31 The Theme of Competition: The Contest (ὁ ἀγών) 34 Agon and Medicine 35 Poetic Plot and History: A case for the probable 44 Phases of the agon in Thucydides 48 Structuring the Agon 50 Rationality 53 On common knowledge 58 Exogenous and Endogenous 61 From Narrative to Games 63 Clock, Board and Players 66 Rules and Endgame 67 Chapter 1 – Strategic Games – Normal Form 70 The History as a game 70 Dominance - The First Invasion of Attica (431BC) 74 Players, Actions and Preferences 78 Actions 80 Preferences 81 Preferences and Payoffs 85 Normal form representation 88 Agis, son of Archidamos (411BC) 92 Lamachus’ Proposal (415 BC) 93 Demosthenes’ Counterfactual (413 BC) 96 Descriptive Theory 98 Types of Strategic Games with Ordinal Preferences 100 Solution Theory 101 Zero-sum Games (Constant Sum Games) 103 The Sea battle in the Great Harbour at Syracuse (413 BC) 104 Ring Composition and Chiasmus 107 The board - Type of battle 108 Players, Actions and Preferences 110 Actions 112 Preferences and Payoffs 116 What then is the preference relation of a fleet? 117 4 Strategic Game with Cardinal Payoffs (7.70-71) 119 Descriptive Theory (7.70) 119 Solution Theory (7.71) 125 Mixed Strategy 129 Sight and Judgment 131 The Diagnosis of a Worthy Contest 140 Chapter 2 - Dynamic Games - Extensive Form 144 Agon and Law 145 Negotiation 149 The Spartan Negotiation (1.126 - 146) 151 Players, Actions and Preferences 151 Payoffs 155 Escalation 155 Melian Dialogue (5.84-116) 158 Board – Temporal structure 158 Descriptive Theory 161 Solution Theory 162 Melians Reject the Offer 164 Siege Warfare 166 The contest of Wall/ Counter-wall (6.93.4 - 7.6) 168 Preparing to begin the contest 168 The Race of Wall/Counter-wall (6.99 - 7.6) 172 The board 172 Players, Actions and Preferences 174 Players 174 Actions 175 Preferences 176 Phase One of Wall/Counter-wall (6.98.2 - 100) 179 Phase Two of Wall/Counter-wall (6.101-102) 181 Summary of Preferences 182 Phase Three of Wall/Counter-wall (6.103 – 7.6) 184 Shifting Strategies (6.103 – 7.1) 184 Summary of Preferences 186 Wall/Counter-wall Resumed (7.2- 7.6) 187 Duels 187 Descriptive Theory 189 The Mistakes 195 Majority Voting in Classical Athens 199 Majority Voting in Thucydides 200 The Council of War in Thucydides (6.47-50.1) 204 The Council of War 206 Why Alcibiades and not Nicias? 211 Chapter 3 - Incomplete Information, Bounded Rationality 213 First and Second Mover Models 213 Bounded Rationality 236 Anger and Restraint 237 The Mytilene Episode (3.1-3.50) 237 Multiselves model 240 The Speeches 241 Cleon’s Speech 242 Diodotus’ Speech 243 Anger and Naivete 244 The first as the worst 244 5 A feasible set 253 First period preferences 253 Second period preferences 254 Rules of Rhetoric 256 The Decision Rule 257 The Period 1 proposal versus the Period 2 proposal 260 Monopolistic environment 261 Case for the sophisticated decision maker 261 Case for the naive decision maker 265 Randomization 287 Cleon’s no deterrence 288 Shock wave 290 The Drama 291 The Chance Wind 292 Conclusion 294 Bibliography 296 Appendix 322 6 List of Tables and Images Table 1 ____________________________________________________ 88 Table 2 ____________________________________________________ 89 Table 3 ____________________________________________________ 89 Table 4 ___________________________________________________ 100 Table 5 ___________________________________________________ 101 Table 6 ___________________________________________________ 122 Table 7: Player 1 best responses, Player 2 best responses __________ 123 Table 8 ___________________________________________________ 123 Table 9 ___________________________________________________ 129 Figure A ___________________________________________________ 68 Figure B ___________________________________________________ 76 Figure C ___________________________________________________ 77 Figure D: Athens – The city and its surroundings ___________________ 80 Figure E: The Boring Woman __________________________________ 103 Figure F __________________________________________________ 108 Figure G __________________________________________________ 110 Figure H: winning, indifferent, losing ____________________________ 128 Figure I ___________________________________________________ 134 Figure J __________________________________________________ 134 Figure K __________________________________________________ 135 Figure L __________________________________________________ 154 Figure M __________________________________________________ 162 Figure N __________________________________________________ 174 Figure O __________________________________________________ 190 Figure P __________________________________________________ 191 Figure Q __________________________________________________ 192 Figure R __________________________________________________ 193 Figure S __________________________________________________ 193 Figure T __________________________________________________ 194 Figure U __________________________________________________ 224 7 Abreviations Aesch. Aeschylus Ain. Tact. Aineias ‘the Tactician’ Aischin. Aischines Ar. Aristophanes Arist. Aristotle Arr. Arrian Ath. Pol. Athenaion Politeia (Athenian Constitution, att. to Aristotle) bk book of Thucydides (1 of 8) Dem. Demosthenes Diod. Diodorus of Sicily Eur. Euripides HC Historia Conscribenda, Lucian Hdt. Herodotus Hell. Hellenika, Xenophon Hipp. Hippocrates Hom. Homer Lys. Lysias O. Olympian ode, Pindar Oxy. Hist. The Oxyrhynchos Historian Paus. Pausanias Plut. Plutarch Pol. Polybius Soph. Sophocles Strab. Strabo Tac. Tacitus Thuc. Thucydides Xen. Xenophon Alberti G. B. Alberti, ed. Thucydidis Historiae 3 vols. (Roma, 1972-2000) Beloch K. J. Beloch, Griechische Geschichte, 4 vols. in 8, second edn. (1912-27) Bétant E.-A. Bétant, Lexicon Thucydideum, 2 vols. (Geneva, 1843) BNJ Brill’s New Jacoby (online resource, 2006) Classen/Steup Thukydides erklärt von J. Classen, bearbeitet von J. Steup, 3rd to 5th edns. (Berlin, 1920-22) CT S. Hornblower, A Commentary on Thucydides, 3 vols. (Oxford, 1991, 1996, 2008). Cited as CT 1, 2, 3. Crawley Thucydides: History of the Peloponnesian War, tr. R. Crawley (orig. pub. 1874, 1997) De Ste Croix, OPW G. E. M. de Ste Croix, The Origins of the Peloponnesian War (London, 1972) 8 DK H. Diels and W. Kranz (eds.), Die Fragmente der Vorsokratiker, 6th edn. 4 vols. (Berlin, 1952) FGrHist F. Jacoby, Die Fragmente der griechischen Historiker, 15 vols. (Berlin, 1923-58) Hammond Thucydides: The Peloponnesian War, tr. M. Hammond (Oxford, 2009) HCT A. W. Gomme, A. Andrewes, and K. J. Dover, A Historical Commentary on Thucydides, 5 vols. (Oxford, 1945-81) IG Inscriptiones Graecae LS H. G. Liddell and R. Scott, rev. H. Stuart Jones and R. McKenzie, A Greek-English Lexicon, 9th edn. (1940), with Revised Supplement (Oxford, 1968) Marchant
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