This book honors the memory of Tony Atkinson, who made significant contributions to the rigorous study of income inequality, poverty, and redistribution. These essays presented, covering a span of over 30 years of research and scholarship, have been at the forefront of distributional analysis, and many of them are of prime importance for contemporary developments in the real-valued measurement of poverty and inequality, with particular reference to the concepts of fuzzy poverty assessment, vulnerability, heterogeneity/multidimensionality, unit consistency, sub-group decomposability, and dominance criteria. While all of these articles have been previously published-singly or with co-authorship-in a number of professional journals or distinguished edited volumes, this book is greatly enriched by a substantial introductions by the authors, which place the contributions in context, highlights their inter-connectedness, and relates them to the work of Tony Atkinson and other scholars. This book is of intrinsic value to welfare analysts, as well as being a tribute to a very great scholar by a fellow economist.

This book provides a synthesis of some recent issues and an up-to-date treatment of some of the major important issues in distributional analysis that I have covered in my previous book Ethical Social Index Numbers, which was widely accepted by students, teachers, researchers and practitioners in the area. Wide coverage of on-going and advanced topics and their analytical, articulate and authoritative p- sentation make the book theoretically and methodologically quite contemporary and inclusive, and highly responsive to the practical problems of recent concern. Since many countries of the world are still characterized by high levels of income inequality, Chap. 1 analyzes the problems of income inequality measurement in detail. Poverty alleviation is an overriding goal of development and social policy. To formulate antipoverty policies, research on poverty has mostly focused on inco- based indices. In view of this, a substantive analysis of income-based poverty has been presented in Chap. 2. The subject of Chap. 3 is people's perception about income inequality in terms of deprivation. Since polarization is of current concern to analysts and social decisi- makers, a discussion on polarization is presented in Chap. 4.

The combined efforts of the Physicists and the Economists in recent years in a- lyzing and modeling various dynamic phenomena in monetary and social systems have led to encouragingdevelopments,generally classi?ed under the title of Eco- physics. These developmentsshare a commonambitionwith the alreadyestablished ?eld of Quantitative Economics. This volume intends to offer the reader a glimpse of these two parallel initiatives by collecting review papers written by well-known experts in the respective research frontiers in one cover. This massive book presents a unique combination of research papers contributed almost equally by Physicists and Economists. Additional contributions from C- puter Scientists and Mathematicians are also included in this volume. It consists of two parts: The ?rst part concentrates on econophysics of games and social choices and is the proceedings of the Econophys-Kolkata IV workshop held at the Indian Statistical Institute and the Saha Institute of Nuclear Physics, both in Kolkata, d- ing March 9-13, 2009. The second part consists of contributionsto quantitative e- nomics by experts in connection with the Platinum Jubilee celebration of the Indian Statistical Institute. In this connectiona Forewordfor the volume, written by Sankar K. Pal, Director of the Indian Statistical Institute, is put forth. Both parts specialize mostly on frontier problems in games and social choices. The?rst partofthebookdealswith severalrecentdevelopmentsineconophysics. Game theory is integral to the formulation of modern economic analysis. Often games display a situation where the social optimal could not be reached as a - sult of non co-operation between different agents.

'An Outline of Financial Economics' presents a systematic treatment of the theory and methodology of finance and economics. The book follows an analytical and geometric methodology, explaining technical terms and mathematical operations in clear, nontechnical language, and providing intuitive explanations of the mathematical results. The text begins with a discussion of financial instruments, which form the basis of finance theory, and goes on to analyze bonds - which are regarded as fixed income securities - in a simple framework and to discuss the valuation of stocks and cash flows in detail. Highly relevant topics such as attitudes toward risk, uncertainty, financial structure of a firm, stochastic dominance, portfolio management, option pricing and conditions for non-arbitrage are analyzed explicitly. Because of its wide coverage and analytical, articulate and authoritative presentation, 'An Outline of Financial Economics' will be an indispensable book for finance researchers and undergraduate and graduate students in fields such as economics, finance, econometrics, statistics and mathematics.

Econophysics of Games and Social Choices.- Kolkata Paise Restaurant Problem in Some Uniform Learning Strategy Limits.- Cycle Monotonicity in Scheduling Models.- Reinforced Learning in Market Games.- Mechanisms Supporting Cooperation for the Evolutionary Prisoner's Dilemma Games.- Economic Applications of Quantum Information Processing.- Using Many-Body Entanglement for Coordinated Action in Game Theory Problems.- Condensation Phenomena and Pareto Distribution in Disordered Urn Models.- Economic Interactions and the Distribution of Wealth.- Wealth Redistribution in Boltzmann-like Models of Conservative Economies.- Multi-species Models in Econo- and Sociophysics.- The Morphology of Urban Agglomerations for Developing Countries: A Case Study with China.- A Mean-Field Model of Financial Markets: Reproducing Long Tailed Distributions and Volatility Correlations.- Statistical Properties of Fluctuations: A Method to Check Market Behavior.- Modeling Saturation in Industrial Growth.- The Kuznets Curve and the Inequality Process.- Monitoring the Teaching - Learning Process via an Entropy Based Index.- Technology Level in the Industrial Supply Chain: Thermodynamic Concept.- Discussions and Comments in Econophys Kolkata IV.- Contributions to Quantitative Economics.- On Multi-Utility Representation of Equitable Intergenerational Preferences.- Variable Populations and Inequality-Sensitive Ethical Judgments.- A Model of Income Distribution.- Statistical Database of the Indian Economy: Need for New Directions.- Does Parental Education Protect Child Health? Some Evidence from Rural Udaipur.- Food Security and Crop Diversification: Can West Bengal Achieve Both?.- Estimating Equivalence Scales Through Engel Curve Analysis.- Testing for Absolute Convergence: A Panel Data Approach.- Goodwin's Growth Cycles: A Reconsideration.- Human Capital Accumulation, Economic Growth and Educational Subsidy Policy in a Dual Economy.- Arms Trade and Conflict Resolution: A Trade-Theoretic Analysis.- Trade andWage Inequality with Endogenous Skill Formation.- Dominant Strategy Implementation in Multi-unit Allocation Problems.- Allocation through Reduction on Minimum Cost Spanning Tree Games.- Unmediated and Mediated Communication Equilibria of Battle of the Sexes with Incomplete Information.- A Characterization Result on the Coincidence of the Prenucleolus and the Shapley Value.- The Ordinal Equivalence of the Johnston Index and the Established Notions of Power.- Reflecting on Market Size and Entry under Oligopoly.

This book analyzes the following four distinct, although not dissimilar, areas of social choice theory and welfare economics: nonstrategic choice, Harsanyi's aggregation theorems, distributional ethics and strategic choice. While for aggregation of individual ranking of social states, whether the persons behave strategically or non-strategically, the decision making takes place under complete certainty; in the Harsanyi framework uncertainty has a significant role in the decision making process. Another ingenious characteristic of the book is the discussion of ethical approaches to evaluation of inequality arising from unequal distributions of achievements in the different dimensions of human well-being. Given its wide coverage, combined with newly added materials, end-chapter problems and bibliographical notes, the book will be helpful material for students and researchers interested in this frontline area research. Its lucid exposition, along with non-technical and graphical illustration of the concepts, use of numerical examples, makes the book a useful text.

In this book we are concerned with income profile based ethical social index numbers. An ethical index is designed from an explicit social evaluation function with a specific purpose in mind. For example, an ethical relative inequality index determines the fraction of total income that could be saved without any welfare loss if society distri buted incomes equally. Ethical indices contrast with descriptive indices which are de rived without using any concept of social welfare. Needless to say, ethical indices are not meant to supplant descriptive indices, rather they are constructed with different aims. We begin Chapter 1 with a formal discussion on the concept of a social evaluation function. In the main body of this chapter we consider the problem of ranking income profiles using a social evaluation function. In Chapter 2 we set about analyzing alter native approaches to the measurement of inequality. In Chapter 3 we focus our attention on the Gini index, the most frequently used index of inequality, and its extensions. In Chapter 4 we formulate the notion of an ethical distance function that measures welfare of one population relative to another. Chapter 5 is devoted to quantifications and discussions of alternative definitions of relative deprivation put forward by Runci man(1966).

This book provides a synthesis of some recent issues and an up-to-date treatment of some of the major important issues in distributional analysis that I have covered in my previous book Ethical Social Index Numbers, which was widely accepted by students, teachers, researchers and practitioners in the area. Wide coverage of on-going and advanced topics and their analytical, articulate and authoritative p- sentation make the book theoretically and methodologically quite contemporary and inclusive, and highly responsive to the practical problems of recent concern. Since many countries of the world are still characterized by high levels of income inequality, Chap. 1 analyzes the problems of income inequality measurement in detail. Poverty alleviation is an overriding goal of development and social policy. To formulate antipoverty policies, research on poverty has mostly focused on inco- based indices. In view of this, a substantive analysis of income-based poverty has been presented in Chap. 2. The subject of Chap. 3 is people's perception about income inequality in terms of deprivation. Since polarization is of current concern to analysts and social decisi- makers, a discussion on polarization is presented in Chap. 4.

This book analyzes the following four distinct, although not dissimilar, areas of social choice theory and welfare economics: nonstrategic choice, Harsanyi's aggregation theorems, distributional ethics and strategic choice. While for aggregation of individual ranking of social states, whether the persons behave strategically or non-strategically, the decision making takes place under complete certainty; in the Harsanyi framework uncertainty has a significant role in the decision making process. Another ingenious characteristic of the book is the discussion of ethical approaches to evaluation of inequality arising from unequal distributions of achievements in the different dimensions of human well-being. Given its wide coverage, combined with newly added materials, end-chapter problems and bibliographical notes, the book will be helpful material for students and researchers interested in this frontline area research. Its lucid exposition, along with non-technical and graphical illustration of the concepts, use of numerical examples, makes the book a useful text.

Cooperative game theory deals with situations where objectives of participants of the game are partially cooperative and partially conflicting. It is in the interest of participants to cooperate in the sense of making binding agreements to achieve the maximum possible benefit. When it comes to distribution of benefit/payoffs, participants have conflicting interests. Such situations are usually modelled as cooperative games. While the book mainly discusses transferable utility games, there is also a brief analysis of non-transferable utility games. Alternative solution concepts to cooperative game theoretic problems are presented in chapters 1-9 and the next four chapters present issues related to computations of solutions discussed in the earlier chapters. The proofs of all results presented in the book are quite explicit. Additionally the mathematical techniques employed in demonstrating the results will be helpful to those who wish to learn application of mathematics for solving problems in game theory.