UvA-DARE (Digital Academic Repository) Play without regret Galeazzi, P. Publication date 2017 Document Version Final published version License Other Link to publication Citation for published version (APA): Galeazzi, P. (2017). Play without regret. General rights It is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons). Disclaimer/Complaints regulations If you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: https://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible. UvA-DARE is a service provided by the library of the University of Amsterdam (https://dare.uva.nl) Download date:06 Oct 2021 Paolo Galeazzi Play Without Regret Play Without Regret Without Play i pska Paolo Galeazzi Paolo Play Without Regret Paolo Galeazzi Play Without Regret ILLC Dissertation Series DS-2017-01 For further information about ILLC-publications, please contact Institute for Logic, Language and Computation Universiteit van Amsterdam Science Park 107 1098 XG Amsterdam phone: +31-20-525 6051 e-mail: [email protected] homepage: http://www.illc.uva.nl/ The investigations were supported by the European Research Council under the European Research Community’s Seventh Framework Programme (FP7/2007- 2013)/ERC Grant agreement no.283963. Copyright c 2017 by Paolo Galeazzi Cover design by Paolo Galeazzi. Picture by Diego Fedele. Printed and bound by Ipskamp Drukkers. ISBN: 978-94-028-0463-8 Play Without Regret Academisch Proefschrift ter verkrijging van de graad van doctor aan de Universiteit van Amsterdam op gezag van de Rector Magnificus prof. dr. ir. K.I.J. Maex ten overstaan van een door het College voor Promoties ingestelde commissie, in het openbaar te verdedigen in de Aula der Universiteit op woensdag 25 januari 2017, te 11.00 uur door Paolo Galeazzi geboren te Venetië, Italië Promotiecommisie Promotor: Prof. dr. S.J.L. Smets Universiteit van Amsterdam Co-promotor: Dr. A. Baltag Universiteit van Amsterdam Overige leden: Prof. dr. M. van Lambalgen Universiteit van Amsterdam Prof. dr. R.A.M. van Rooij Universiteit van Amsterdam Prof. dr. J. van Eijck Universiteit van Amsterdam Dr. J. Szymanik Universiteit van Amsterdam Prof. dr. R. Bradley London School of Economics and Political Science Dr. K.J.S. Zollman Carnegie Mellon University Dr. A. Perea Universiteit van Maastricht Faculteit der Natuurwetenschappen, Wiskunde en Informatica The results in this thesis come from the following works. 1. Chapter 4 is based on: Galeazzi, P. and Lorini, E. (2016). Epistemic logic meets epistemic game theory: a comparison between multi-agent Kripke models and type spaces. Synthese, 193 (7):2097-2127. 2. Chapter 5 and part of Chapter 7 are based on: Galeazzi, P. and Franke, M. (2016). Smart Representations: Rationality and Evolution in a Richer Environment. To appear in Philosophy of Science. 3. Chapter 6 is based on ongoing research with Mathias W. Madsen. 4. Chapter 8 is based on ongoing research with Zoi Terzopoulou. vii viii to everyone I have neglected while I was busy with this dissertation (myself included) ix Contents Acknowledgments xv 1 Introduction 1 1.1 Subjective Expected Utility Maximization . .3 1.2 Criticisms of SEU . .4 1.3 A Brief Overview . .6 1.4 Our Contributions . .7 I Background 9 2 Background on Rational Choice 11 2.1 From the Early Days to Savage . 11 2.2 Non-Bayesian and Non-Expected Utility Theories . 19 2.3 Ecological Rationality . 39 3 Background on (Evolutionary) Game Theory 43 3.1 Game Theory . 43 3.2 Evolutionary Game Theory . 58 3.3 An Important Example . 68 4 Epistemic Structures for Rationality 75 4.1 Introduction . 75 4.2 Models With Belief . 77 4.2.1 Language . 77 4.2.2 Semantics . 77 4.2.2.1 Doxastic models . 77 4.2.2.2 Type spaces . 79 4.2.3 Correspondence . 81 xi xii Contents 4.3 Models With Belief and Knowledge . 84 4.3.1 Language . 84 4.3.2 Semantics . 84 4.3.2.1 Type spaces . 84 4.3.2.2 Epistemic-doxastic models . 85 4.3.3 Correspondence . 86 4.3.4 Examples . 88 4.3.5 Discussion . 89 4.3.5.1 On the knowledge operator . 90 4.3.5.2 Qualitative vs. quantitative type spaces . 92 4.4 Axiomatization . 93 4.5 Probabilistic Extension . 99 4.5.1 Language . 99 4.5.2 Semantics . 100 4.5.2.1 Type spaces . 100 4.5.2.2 Epistemic-probabilistic models . 100 4.5.3 Correspondence . 101 4.6 Conclusion . 102 II Evolutionary Analysis 105 5 The Game of Life 107 5.1 The Behavioral Gambit . 107 5.2 Choice Principles: A General Discussion . 108 5.3 On the Rationality of Choice Principles . 113 5.4 The Game of Life . 114 5.5 The Model . 115 5.6 A Bold Alternative to the Alternatives . 116 5.7 Results . 119 5.7.1 Simulation results . 119 5.7.2 Analytical results . 121 5.8 Extensions . 122 5.8.1 More preference types . 122 5.8.2 More actions . 123 5.8.3 Solitary decisions . 125 5.9 Conclusion . 126 5.9.1 Subjective preferences or choice principles? . 126 5.9.2 Precise and imprecise beliefs . 127 5.10 Appendix: Proofs . 128 Contents xiii 6 Learning Players’ Types 137 6.1 The Learning Model . 138 6.2 Intermezzo: A Simple Extraction . 140 6.3 The Game of Life with Incomplete Information . 141 6.4 Symmetry and Learning . 144 6.5 Strong Informativity . 145 6.6 The Set of Strongly Informative Games . 149 6.7 Asymmetric Equilibria and Behavioral Assumptions . 155 6.8 Discrete and Continuous Fitness . 159 6.9 Conclusion . 160 6.10 Appendix: Proofs . 160 7 Evolution and Learning 167 7.1 The Game of Life with Learning . 167 7.2 Play Without Regret . 168 7.3 Regret What? . 169 7.4 Conclusion . 171 7.5 Appendix: Proofs . 171 8 A Theory of Rationality 179 8.1 The Traveler’s Dilemma Case . 179 8.2 A Modest Proposal . 180 8.3 Relief Maximization . 184 8.4 From an Evolutionary Point of View . 188 8.5 Nested and Weighted Principles . 189 8.6 The Power of Context Dependency . 191 8.7 Conclusion . 195 9 Conclusion 197 Bibliography 201 Abstract 213 Samenvatting 215 Acknowledgments First of all, I want to thank my supervisors, Sonja Smets and Alexandru Baltag, for their valuable suggestions and their support along these years. The complete trust that I received from Sonja and Alex in developing my research directions is still a mystery to me, but it has certainly been a key factor for this dissertation. I hope I have been able to use their trust and their support at best. Second, I am very grateful to Michiel van Lambalgen, Robert van Rooij, Jan van Eijck, Jakub Szymanik, Richard Bradley, Andrés Perea, and Kevin Zollman for accepting to be members of my thesis committee, which involves the heavy task of reading and understanding my exotic English sentences. In addition, I consider all the exchanges that I had with them extremely pleasant and encouraging from a personal point of view, and greatly profitable for my research. The list of persons that I met during the Ph.D. and that contributed to the development of the ideas which gave birth to this thesis is still very long. I am surely the main responsible for the final outcome, and, hence, the first person to blame. However, the contribution of Michael Franke has been essential in these years. Coming from different fields, when I proposed him to work on my strange intuitions about the evolution of choice principles, he had absolutely no need or obligation (and probably even no much time) to give me any attention. I consider the fact that we immediately started working together not only the turning point of my Ph.D., but also a unique personal pleasure. It is likely that most of my actual research wouldn’t even have begun without Michael. Mathias Madsen has also importantly contributed to the improvement of this thesis. It was my great pleasure to develop the parts about the learning with him, we ended up learning a lot together, and I believe his brightness clearly shines through those pages. I want to greatly thank Emiliano Lorini for inviting me at the University of Toulouse. That visit allowed me to enhance the research on type spaces and Kripke models which I had started for my master thesis, and which is contained here in Chapter 4. xv xvi Acknowledgments I am also very thankful to Zoi Terzopoulou, who had the insane bravery to trust me and to ask for a project on decision theory. That project gave me the opportunity to develop some ideas on context-dependent rationality that I would have certainly forgotten otherwise. She has been a very smart and interested student, and I hope she had as much fun as I had during the project. The outcome of my research would have also been considerably different with- out the many discussions that I had the priviledge to entertain with all the persons that shared their time and their views with me along these four years. In this re- spect, I am especially indebted to Pierpaolo Battigalli, Erik Quaeghebeur, Teddy Seidenfeld, and Michiel van Lambalgen.