Thinking before Acting. Intentions, Logic, Rational Choice [PhD Thesis]

215 Pages·2006·2.784 MB·English

by  Olivier Roy

Thinking before Acting
Intentions, Logic, Rational Choice
Olivier Roy

Thinking before Acting
Intentions, Logic, Rational Choice
ILLC Dissertation Series DS-2008-03
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Thinking before Acting
Intentions, Logic, Rational Choice
Academisch Proefschrift
ter verkrijging van de graad van doctor aan de
Universiteit van Amsterdam
op gezag van de Rector Magnificus
prof.dr. D.C. van den Boom
ten overstaan van een door het college voor
promoties ingestelde commissie, in het openbaar
te verdedigen in de Aula der Universiteit
op dinsdag 26 februari 2008, te 10.00 uur
door
Olivier Roy
geboren te Sept-Iles, Qu´ebec, Canada.
Promotiecommissie:
Promotor:
Prof.dr. J.F.A.K. van Benthem
Co-promotor:
Prof.dr. M.V.B.P.M. van Hees
Overige leden:
Prof. dr. M. Bratman
Prof. dr. R. Bradley
Prof. dr. K. R. Apt
Prof. dr. F. Veltman
Faculteit der Natuurwetenschappen, Wiskunde en Informatica
The investigations were supported by the Fond Qu´eb´ecois de la Recherche sur la
Soci´et´e et la Culture (bourse # 93233), and by the Conseil de la Recherche en
Science Humaine du Canada (bourse # 752-2006-0345).
Cover design by Lin de Mol.
Original artwork on the back cover : ‘Tr´a’, 2004 C-print, 20 x 30 cm.
Copyright (cid:13)c Lin de Mol, Courtesy Galery Lumen Travo
Printed and bound by Printpartners Ipskamp.
Copyright (cid:13)c 2008 by Olivier Roy
ISBN: 978–90–5776–174–4
`
A Christine, Chantal et Omer
v

Contents
Acknowledgments xi
1 Introduction 1
1.1 Instrumental rationality, decision and game theory . . . . . . . . . 3
1.1.1 Decision theory: rational decision making under uncertainty 3
1.1.2 Game theory: reasoning with mutual expectations . . . . . 5
1.2 Intentions and planning agency . . . . . . . . . . . . . . . . . . . 7
1.3 Dynamic epistemic logic . . . . . . . . . . . . . . . . . . . . . . . 11
1.4 Outline of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . 14
2 Intentions and individual decision making 17
2.1 Extensive decision problems . . . . . . . . . . . . . . . . . . . . . 18
2.2 Actions- and outcomes-intentions in extensive decision problems . 21
2.3 Intentions with counterfactual consequences . . . . . . . . . . . . 26
2.4 Ideal and resources-bounded agents . . . . . . . . . . . . . . . . . 29
2.5 From extensive to strategic representations . . . . . . . . . . . . . 31
2.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3 Intentions and coordination in strategic games 35
3.1 Intentions in strategic interactions . . . . . . . . . . . . . . . . . . 36
3.2 Coordination in Hi-Lo games . . . . . . . . . . . . . . . . . . . . . 39
3.3 Intentions and rational expectations . . . . . . . . . . . . . . . . . 42
3.4 Epistemic models for games with intentions . . . . . . . . . . . . 45
3.5 Coordination with payoff-compatible intentions . . . . . . . . . . 48
3.6 Stackelberg heuristic and intention-based coordination . . . . . . 54
3.7 Limits of payoff-compatibility of intentions . . . . . . . . . . . . . 56
3.8 A general account of intention-based coordination . . . . . . . . . 57
3.9 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.10 Appendix - Solution concepts . . . . . . . . . . . . . . . . . . . . 62
vii
4 Intentions and transformations of strategic games 63
4.1 Ruling out options . . . . . . . . . . . . . . . . . . . . . . . . . . 64
4.2 Grouping redundant options . . . . . . . . . . . . . . . . . . . . . 71
4.3 Grouping and ruling out options . . . . . . . . . . . . . . . . . . . 76
4.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
5 Logics for practical reasoning with intentions 83
5.1 Preliminaries: modal logic for preferences . . . . . . . . . . . . . . 83
5.1.1 Preference models and language . . . . . . . . . . . . . . . 84
5.1.2 Expressive power . . . . . . . . . . . . . . . . . . . . . . . 86
5.1.3 Axiomatization . . . . . . . . . . . . . . . . . . . . . . . . 88
5.2 Logic for games with intentions . . . . . . . . . . . . . . . . . . . 89
5.2.1 Language for epistemic game models with intentions . . . 89
5.2.2 Expressive power . . . . . . . . . . . . . . . . . . . . . . . 93
5.2.3 Axiomatization . . . . . . . . . . . . . . . . . . . . . . . . 102
5.3 Transformations of games with intentions . . . . . . . . . . . . . . 102
5.3.1 Dynamic language . . . . . . . . . . . . . . . . . . . . . . 104
5.3.2 Axiomatization . . . . . . . . . . . . . . . . . . . . . . . . 106
5.3.3 Expressive power . . . . . . . . . . . . . . . . . . . . . . . 108
5.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
5.5 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
5.5.1 Bisimulation and modal equivalence for L . . . . . . . . . 125
P
5.5.2 More on lifted relations in L . . . . . . . . . . . . . . . . 126
P
5.5.3 More on the expressive power of L . . . . . . . . . . . . 127
GF
5.5.4 Proof of Theorem 5.2.13 . . . . . . . . . . . . . . . . . . . 128
5.5.5 Complete axiom system for DL . . . . . . . . . . . . . . 133
GF
5.5.6 Dynamic characterization of Nash equilibrium. . . . . . . . 134
6 Hybrid pragmatism, acceptances and norms on intentions 137
6.1 Constraints on rational intentions . . . . . . . . . . . . . . . . . . 138
6.2 Cognitivism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
6.2.1 The functionalist view on beliefs . . . . . . . . . . . . . . . 142
6.2.2 Constraints on rational beliefs . . . . . . . . . . . . . . . . 143
6.2.3 Weak, intermediate and strong cognitivism . . . . . . . . . 145
6.2.4 Rational intentions from rational beliefs . . . . . . . . . . 146
6.2.5 A general concern against cognitivism . . . . . . . . . . . . 150
6.3 Acceptances in deliberation . . . . . . . . . . . . . . . . . . . . . 152
6.3.1 Accepting or taking for granted in deliberation . . . . . . . 152
6.3.2 The adjusted background of deliberation . . . . . . . . . . 155
6.3.3 Requirements on the background of deliberation . . . . . . 155
6.4 Hybrid Pragmatism . . . . . . . . . . . . . . . . . . . . . . . . . . 158
6.4.1 Intentions and acceptances . . . . . . . . . . . . . . . . . . 158
6.4.2 The absent-minded cyclist revisited . . . . . . . . . . . . . 159
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