Econophysics of the Kolkata Restaurant Problem and Related Games

Transcription

1 Econophysics of the Kolkata Restaurant Problem and Related Games

2 New Economic Windows Series editors MARISA FAGGINI, MAURO GALLEGATI, ALAN P. KIRMAN, THOMAS LUX Series Editorial Board Jaime Gil Aluja Departament d Economia i Organització d Empreses, Universitat de Barcelona, Barcelona, Spain Fortunato Arecchi Dipartimento di Fisica, Università degli Studi di Firenze and INOA, Florence, Italy David Colander Department of Economics, Middlebury College, Middlebury, VT, USA Richard H. Day Department of Economics, University of Southern California, Los Angeles, USA Steve Keen School of Economics and Finance, University of Western Sydney, Penrith, Australia Marji Lines Dipartimento di Scienze Statistiche, Università degli Studi di Udine, Udine, Italy Alfredo Medio Dipartimento di Scienze Statistiche, Università degli Studi di Udine, Udine, Italy Paul Ormerod Directors of Environment Business-Volterra Consulting, London, UK Peter Richmond School of Physics, Trinity College, Dublin 2, Ireland J. Barkley Rosser Department of Economics, James Madison University, Harrisonburg, VA, USA Sorin Solomon Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem, Israel Pietro Terna Dipartimento di Scienze Economiche e Finanziarie, Università degli Studi di Torino, Torino, Italy Kumaraswamy (Vela) Velupillai Department of Economics, National University of Ireland, Galway, Ireland Nicolas Vriend Department of Economics, Queen Mary University of London, London, UK Lofti Zadeh Computer Science Division, University of California Berkeley, Berkeley, CA, USA More information about this series at

3 Bikas K. Chakrabarti Arnab Chatterjee Asim Ghosh Sudip Mukherjee Boaz Tamir Econophysics of the Kolkata Restaurant Problem and Related Games Classical and Quantum Strategies for Multi-agent, Multi-choice Repetitive Games 123

4 Bikas K. Chakrabarti Condensed Matter Physics Division Saha Institute of Nuclear Physics Kolkata and Economic Research Unit n Statistical Institute Kolkata Arnab Chatterjee Condensed Matter Physics Division Saha Institute of Nuclear Physics Kolkata and TCS Innovation Labs Delhi Asim Ghosh Department of Computer Science Aalto University School of Science Espoo Finland and Raghunathpur College Purulia Sudip Mukherjee Department of Physics Barasat Government College Kolkata and Condensed Matter Physics Division Saha Institute of Nuclear Physics Kolkata Boaz Tamir Department of Science Technology and Society, Faculty of Interdisciplinary Studies Bar-Ilan University Ramat-Gan Israel and Iyar, The Israeli Institute for Advanced Research Zikhron Yaakov Israel ISSN X ISSN (electronic) New Economic Windows ISBN ISBN (ebook) DOI / Library of Congress Control Number: Springer International Publishing AG 2017 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

5 Preface The Kolkata Restaurant Problem or more specifically the Kolkata Paise Restaurant (KPR) problem is a repetitive many-choice and many-agent game where the players collectively learn from past experience, and the identification of successful strategies help to avoid the crowd in order to grab the best (minority choice) opportunity available. Although the binary-choice many-agent games, called minority games, have been studied earlier, these many-choice games have many dimensions, and the successful strategies here can have intriguing features. Detailed studies on several stochastic strategies, which ensure maximum utilization of the resources, have been made. These are mostly classical (using statistical physics tricks). Quantum strategies are also being formulated with interesting features. This book intends to give an introduction on this recent development. Along with the main text on these interdisciplinary developments, we have included six appendices for the benefit of the readers. Five of them are invited contributions from our colleagues: Statistical Physics: A Brief Introduction by Purusattam Ray (Institute of Mathematical Sciences, Chennai), Quantum Mechanics: A Brief Introduction by Parthasarathi Mitra (Saha Institute of Nuclear Physics, Kolkata), Game Theory (Classical): A Brief Introduction by Priyodorshi Banerjee (n Statistical Institute, Kolkata), Manipushpak Mitra (n Statistical Institute, Kolkata) and Conan Mukherjee (Lund University, Lund, n Institute of Technology Bombay, Mumbai), Minority Game: An Overview and Recent Results by V. Sasidevan (Frankfurt Institute for Advanced Studies, Frankfurt), and Extending KPR Problem to Dynamic Matching in Mobility Markets by Layla Martin and Paul Karaenke (Technical University of Munich, Munich). We are extremely thankful for their contributions to this volume. Another appendix on Econophysics: A Brief Introduction has also been added by us. Each chapter, including of course the appendices, contains sufficient introductory materials, with references to other chapters or appendices for details, so that the reader can choose each chapter almost independently. We are grateful to our collaborators Soumyajyoti Biswas, Anindya S. Chakrabarti, Anirban Chakraborti, Damien Challet, Daniele De Martino, Deepak Dhar, Matteo Marsili, Tapan Naskar, V. Sasidevan, and Yi-Cheng Zhang for their v

6 vi Preface collaborations in the development of this and related game models. We are also grateful to Mauro Gallegati and other editors of the New Economic Windows series for their encouragement to publish this book in their esteemed series. This book is addressed to students and researchers in economics (game theory and model games), physics (statistical physics, quantum mechanics), and computer science (job scheduling, etc). We hope they will find material here sufficiently exciting and useful for inspiring researches in these directions. Kolkata, Delhi, Espoo, Finland Kolkata, Ramat-Gan, Israel March 2017 Bikas K. Chakrabarti Arnab Chatterjee Asim Ghosh Sudip Mukherjee Boaz Tamir

7 Acknowledgements We thank P. Banerjee, L. Martin, P. Karaenke, M. Mitra, P. Mitra, C. Mukherjee, P. Ray, and V. Sasidevan for contributing appendices to this book. We would like to thank our collaborators S. Biswas, A.S. Chakrabarti, A. Chakraborti, D. Challet, D. De Martino, D. Dhar, M. Marsili, T. Naskar, V. Sasidevan, and Y.-C. Zhang for collaborations and discussions at various stages. We are also grateful to S. Biswas, A.S. Chakrabarti, D. Ghosh, and L. Martin for their help by providing us with their yet unpublished results of investigations regarding extended Kolkata Restaurant problems in various contexts, through preprints and thesis copy (private communication) and checking our summary of their results, given in Chap. 7. vii

8 Contents 1 Introduction Background Minority Game Kolkata Restaurant Problem Motivation of the Book Plan of the Book Kolkata Paise Restaurant Problem Introduction Stochastic Learning Strategies Random Choice Strategies Rank Dependent Strategies Strict Crowd-Avoiding Case Stochastic Crowd Avoiding Case Convergence to a Fair Social Norm with Deterministic Strategies A Fair Strategy Asymptotically Fair Strategy Summary and Discussion Phase Transition in the Kolkata Paise Restaurant Problem Introduction The Models Results from Numerical Simulations Model A Model B Analytical Treatment of the Models in Mean Field Case Approximate Analysis of the Critical Point and Faster-Is-Slower Effect Analysis of the Finite Size Effects on the Time to Reach the Absorbing State Summary and Discussions ix

9 x Contents 4 Zipf s Law from Kolkata Paise Restaurant Problem Introduction Model Results Distribution of Sizes Utilization Evolution with Fitness Empirical Evidences Summary and Discussions Minority Game and Kolkata Paise Restaurant Problem Introduction Strategy of the Agents Uniform Approximation in Guessing the Excess Crowd Nonuniform Guessing of the Excess Crowd Following an Annealing Schedule Effect of Random Traders Summary and Discussions From Classical Games, the Kokata Paise Restuarant Game, to Quantum Games A Short Introduction to Classical Games Definitions and Preliminaries Repeated Games Games and Evolution Theory KPR Some Simple KPR Results Phase Transition Minority Games KPR Non-stochastic Quantum Games Quantum Strategies Nash Equilibrium in Quantum Games Quantum Coin Tossing and Bit Commitment Strong and Weak Coin Tossing Quantum Games and Semidefinite Programming Quantum KPR Summary Some Recent Developments: A Brief Discussion KPR Under Dynamic Setting Reinforcement Learning KPR and Wealth Distribution in Society Summary and Discussions

10 Contents xi Appendix A: Statistical Physics: A Brief Introduction Appendix B: Quantum Mechanics: A Brief Introduction Appendix C: Game Theory (Classical): A Brief Introduction Appendix D: Minority Game: An Overview and Recent Results Appendix E: Extending KPR Problem to Dynamic Matching in Mobility Markets Appendix F: A Brief Discussion on Econophysics References Index