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by Bikas K. Chakrabarti (Author), Arnab Chatterjee (Author), Asim Ghosh (Author), Sudip Mukherjee (Author), Boaz Tamir (Author)
About the Author
Bikas K. Chakrabarti of Saha Institute of Nuclear Physics, Kolkata, India is a Professor of Theoretical Condensed Matter Physics at the Saha Institute of Nuclear Physics and a Visiting Professor of Economics at the Indian Statistical Institute. He has research interests in statistical physics, condensed matter physics, computational physics, and econophysics. He is a Shanti Swarup Bhatnagar awardee and a fellow of the Indian National Science Academy and Indian Academy of Sciences, and he has received the Outstanding Referee award of the American Physical Society. He has coauthored books published by Cambridge University Press, Oxford University Press, Springer, Wiley, etc.
Arnab Chatterjee is a Research Scientist at the TCS Innovation Lab., New Delhi, India. He received his PhD from Jadavpur University in 2008. He has held postdoctoral positions at the International Centre for Theoretical Physics (Trieste, Italy), Centre de Physique Théorique (Marseille, France), Institute for Scientific Interchange (Turin, Italy), and Aalto University (Espoo, Finland). He was also a Visiting Scientist at the Saha Institute of Nuclear Physics, Kolkata, India. He has coauthored two books, published by Cambridge University Press and Wiley. He has extensive research experience in statistical physics and complex systems, complex networks, and socioeconomic systems in general.
Asim Ghosh has been a post-doctoral fellow at the Aalto University, Espoo, Finland, working on Sociophysics and Econophysics. His permanent address is Department of Physics, Raghunathpur College, Purulia 723133, India. He obtained his PhD in 2014 from Calcutta University and has extensive research experience in statistical physics of markets and society, and in particular on the Kolkata Restaurant Problem and the Minority Game using classical tricks.
Sudip Mukherjee of Barasat Government College, Barasat, India holds a Masters degree in Physics from the University of Calcutta. He is a research fellow at Saha Institute of Nuclear Physics, Kolkata and works on quantum spin glasses.
Boaz Tamir of the Faculty of Interdisciplinary Studies, Bar-Ilan University, Ramat Gan, Israel, holds a PhD from the Department of Mathematics of the Weizmann Institute of Science for his work on representation of unitary algebraic groups over p-adic fields and a PhD from Bar-Ilan University for his work on quantum simulation and quantum computation. During the last few years he has published several papers on representations of groups, quantum algorithms, quantum information, bio-information, and philosophy of science. He is currently working on algorithmic methods for community detection in social networks.
About this book
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
1 Introduction
1.1 Background
1.1.1 Minority Game
1.1.2 Kolkata Restaurant Problem
1.2 Motivation of the Book
1.3 Plan of the Book
2 Kolkata Paise Restaurant Problem
2.1 Introduction
2.2 Stochastic Learning Strategies
2.2.1 Random Choice Strategies
2.2.2 Rank Dependent Strategies
2.2.3 Strict Crowd-Avoiding Case
2.2.4 Stochastic Crowd Avoiding Case
2.3 Convergence to a Fair Social Norm with Deterministic Strategies
2.3.1 A ‘Fair’ Strategy
2.3.2 Asymptotically Fair Strategy
2.4 Summary and Discussion
3 Phase Transition in the Kolkata Paise Restaurant Problem
3.1 Introduction
3.2 The Models
3.3 Results from Numerical Simulations
3.3.1 Model A
3.3.2 Model B
3.4 Analytical Treatment of the Models in Mean Field Case
3.4.1 Approximate Analysis of the Critical Point and Faster-Is-Slower Effect
3.4.2 Analysis of the Finite Size Effects on the Time to Reach the Absorbing State
3.5 Summary and Discussions
4 Zipf’s Law from Kolkata Paise Restaurant Problem
4.1 Introduction
4.2 Model
4.3 Results
4.3.1 Distribution of Sizes
4.3.2 Utilization
4.3.3 Evolution with Fitness
4.4 Empirical Evidences
4.5 Summary and Discussions
5 Minority Game and Kolkata Paise Restaurant Problem
5.1 Introduction
5.2 Strategy of the Agents
5.2.1 Uniform Approximation in Guessing the Excess Crowd
5.2.2 Nonuniform Guessing of the Excess Crowd
5.2.3 Following an Annealing Schedule
5.3 Effect of Random Traders
5.4 Summary and Discussions
6 From Classical Games, the Kokata Paise Restuarant Game, to Quantum Games
6.1 A Short Introduction to Classical Games
6.1.1 Definitions and Preliminaries
6.1.2 Repeated Games
6.1.3 Games and Evolution Theory
6.2 KPR
6.2.1 Some Simple KPR Results
6.2.2 Phase Transition
6.2.3 Minority Games
6.2.4 KPR Non-stochastic
6.3 Quantum Games
6.3.1 Quantum Strategies
6.3.2 Nash Equilibrium in Quantum Games
6.3.3 Quantum Coin Tossing and Bit Commitment
6.3.4 Strong and Weak Coin Tossing
6.3.5 Quantum Games and Semidefinite Programming
6.4 Quantum KPR
6.5 Summary
7 Some Recent Developments: A Brief Discussion
7.1 KPR Under Dynamic Setting
7.2 Reinforcement Learning
7.3 KPR and Wealth Distribution in Society
7.4 Summary and Discussions
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
About the series
Even what seems simple in economics generally arises from behavior reflecting the enormous diversity of humanity in terms of knowledge, attitudes, and behaviors, which interact within an enormous range of institutional frameworks. Put briefly, the economy is a complex system.
This complexity arises naturally. Economic agents, be they banks, firms, households, consumers, or investors, act with strategic behavior and foresight by considering outcomes that might result from behavior they might undertake. Furthermore, they continually adjust their market operations, buying decisions, prices, and forecasts to the situations that these operations, decisions, prices, and forecasts together create. This adds a layer of complexity to economics not experienced in the natural sciences.
The recognition of such complexity has resulted in diverse new approaches to the analysis of economic phenomena. After two centuries of preferential study of static equilibrium models, economists are discovering models that contain discontinuity, nonlinearity, and a variety of phenomena that are not so easily predicted or understood.
The New Economics Windows (NEW) series, derived from Massimo Salzano’s ideas and work, comprises books that explore innovative perspectives and components of complexity theory in economics. They have in common an acceptance that economic phenomena should be investigated not as an outcome of deterministic, predictable, and mechanistic dynamics, but as history-dependent, organic, and continually evolving processes.
Research fields covered by the series include in particular (but are not limited to): • Agent-Based Models • Nonlinear Economic Systems • Evolutionary Economics • Econophysics • Chaos Theory • Fractal Analysis• Neuroeconomics• Fuzzy Systems• Network Theory
Series: New Economic Windows
Hardcover: 208 pages
Publisher: Springer; 1st ed. 2017 edition (July 20, 2017)
Language: English
ISBN-10: 3319613510
ISBN-13: 978-3319613512
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