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

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
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 LP . . . . . . . . . 125
5.5.2 More on lifted relations in LP . . . . . . . . . . . . . . . . 126
5.5.3 More on the expressive power of LGF . . . . . . . . . . . . 127
5.5.4 Proof of Theorem 5.2.13 . . . . . . . . . . . . . . . . . . . 128
5.5.5 Complete axiom system for DLGF . . . . . . . . . . . . . . 133
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
6.4.3 Relevance for a deliberation . . . . . . . . . . . . . . . . . 159
6.4.4 Rational intentions from rational acceptances . . . . . . . 160
6.4.5 Acceptances and intentions in deliberation . . . . . . . . . 165
6.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
7 Conclusion 171
7.1 Review of the chapters . . . . . . . . . . . . . . . . . . . . . . . . 171
7.2 Open questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
Index 185
Samenvatting 191
Resume 193
Abstract 195