Econophysics of the Kolkata Restaurant Problem and Related Games

Classical and Quantum Strategies for Multi-agent, Multi-choice Repetitive Games

Bikas K. Chakrabarti, Arnab Chatterjee, Asim Ghosh, Sudip Mukherjee, Boaz Tamir

• Publisher: Springer
• Year: 2017
• Print ISBN:
  9783319613512
• eBook ISBN:
  9783319613529
• Topic: Economics
• Subtopic: Econometrics
• Index: Economics

This book provides the first comprehensive introduction to multi-agent, multi-choice repetitive games, such as the Kolkata Restaurant Problem and the Minority Game. It explains how the tangible formulations of these games, using stochastic strategies developed by statistical physicists employing both classical and quantum physics, have led to very efficient solutions to the problems posed. Further, it includes sufficient introductory notes on information-processing strategies employing both classical statistical physics and quantum mechanics. Games of this nature, in which agents are presented with choices, from among which their goal is to make the minority choice, offer effective means of modeling herd behavior and market dynamics and are highly relevant to assessing systemic risk. Accordingly, this book will be of interest to economists, physicists, and computer scientists alike.

Table of contents

• Preface
• Acknowledgements
• Contents
• 1 Introduction
• 2 Kolkata Paise Restaurant Problem
• 3 Phase Transition in the Kolkata Paise Restaurant Problem
• 4 Zipf's Law from Kolkata Paise Restaurant Problem
• 5 Minority Game and Kolkata Paise Restaurant Problem
• 6 From Classical Games, the Kokata Paise Restuarant Game, to Quantum Games
• 7 Some Recent Developments: A Brief Discussion
• Appendix A Statistical Physics: A Brief Introduction
• A.1 Introduction
• A.2 Specification of Macro and Microstates
• A.3 Statistical Ensembles
• A.4 Different Ensembles in Thermodynamic Systems
• A.4.1 Microcanonical Ensemble (N, V, E)
• A.4.2 Canonical Ensemble (N,V,T)
• A.4.3 Grand Canonical Ensemble (μ,V,T)
• A.5 Statistical Definitions of Thermodynamic Quantities
• A.5.1 Fluid System
• A.5.2 Magnetic System
• A.6 Fluctuation and Macroscopic Quantites
• A.7 Phase Transitions
• A.8 Critical Phenomena
• A.8.1 Fluctuation and Correlation
• A.8.2 Critical Exponents and Universality
• A.9 Nonequilibrium Phase Transitions
• A.9.1 Absorbing-State Phase Transitions
• A.9.2 Other Classes of Absorbing Phase Transitions
• A.10 Self-organized Criticality
• A.10.1 Height Type Sandpile Models
• Appendix B Quantum Mechanics: A Brief Introduction
• Appendix C Game Theory (Classical): A Brief Introduction
• C.1 Introduction
• C.2 Nash Equilibrium
• C.3 The Kolkata Restaurant Problem: The One Shot Version
• C.4 Sub-game Perfect Nash Equilibrium
• C.4.1 Finite Horizon Repeated Games
• C.4.2 Infinite Horizon Repeated Games
• C.5 The Kolkata Restaurant Problem as an Infinitely Repeated Game
• C.6 Cooperative Games
• C.6.1 The Core
• C.6.2 The Shapley Value
• C.7 Conclusion
• Appendix D Minority Game: An Overview and Recent Results
• D.1 To be in the Minority is Beneficial
• D.2 BIMG
• D.3 DIMG
• D.4 Rational Solution: Trapping State and the Co-action Concept
• D.5 Experiments
• D.6 Concluding Remarks
• Appendix E Extending KPR Problem to Dynamic Matching in Mobility Markets
• E.1 Introduction
• E.2 Assumptions
• E.3 Strategies
• E.4 Preliminary Results
• Appendix F A Brief Discussion on Econophysics
• F.1 Introduction
• F.2 Econophysics of Financial Market
• F.2.1 Stylized Facts
• F.2.2 Statistics of Order Books
• F.2.3 Correlation in Financial Market
• F.3 Econophysics of Income and Wealth Distribution
• F.3.1 Data Analysis of the Income and Wealth Distribution
• F.3.2 Models of the Income and Wealth Distribution
• F.4 Summary and Discussion
• Appendix References
• Index