Ken Binmore

It is widely held that Bayesian decision theory is the final word on how a rational person should make decisions. However, Leonard Savage--the inventor of Bayesian decision theory--argued that it would be ridiculous to use his theory outside the kind of small world in which it is always possible to "look before you leap." If taken seriously, this view makes Bayesian decision theory inappropriate for the large worlds of scientific discovery and macroeconomic enterprise. When is it correct to use Bayesian decision theory--and when does it need to be modified? Using a minimum of mathematics, Rational Decisions clearly explains the foundations of Bayesian decision theory and shows why Savage restricted the theory's application to small worlds.The book is a wide-ranging exploration of standard theories of choice and belief under risk and uncertainty. Ken Binmore discusses the various philosophical attitudes related to the nature of probability and offers resolutions to paradoxes believed to hinder further progress. In arguing that the Bayesian approach to knowledge is inadequate in a large world, Binmore proposes an extension to Bayesian decision theory--allowing the idea of a mixed strategy in game theory to be expanded to a larger set of what Binmore refers to as "muddled" strategies.Written by one of the world's leading game theorists, Rational Decisions is the touchstone for anyone needing a concise, accessible, and expert view on Bayesian decision making.

Games are everywhere: Drivers maneuvering in heavy traffic are playing a driving game. Bargain hunters bidding on eBay are playing an auctioning game. The supermarket's price for corn flakes is decided by playing an economic game. This Very Short Introduction offers a succinct tour of the fascinating world of game theory, a ground-breaking field that analyzes how to play games in a rational way. Ken Binmore, a renowned game theorist, explains the theory in a way that is both entertaining and non-mathematical yet also deeply insightful, revealing how game theory can shed light on everything from social gatherings, to ethical decision-making, to successful card-playing strategies, to calculating the sex ratio among bees. With mini-biographies of many fascinating, and occasionally eccentric, founders of the subject--including John Nash, subject of the movie A Beautiful Mind --this book offers a concise overview of a cutting-edge field that has seen spectacular successes inevolutionary biology and economics, and is beginning to revolutionize other disciplines from psychology to political science.About the Series: Oxford's Very Short Introductions offers concise and original introductions to a wide range of subjects--from Islam to Sociology, Politics to Classics, and Literary Theory to History. Not simply a textbook of definitions, each volume provides trenchant and provocative--yet always balanced and complete--discussions of the central issues in a given topic. Every Very Short Introduction gives a readable evolution of the subject in question, demonstrating how it has developed and influenced society. Whatever the area of study, whatever the topic that fascinates the reader, the series has a handy and affordable guide that will likely prove indispensable.

This book lays out foundations for a "science of morals." Binmore uses game theory as a systematic tool for investigating ethical matters. He reinterprets classical social contract ideas within a game-theory framework and generates new insights into the fundamental questions of social philosophy. In contrast to the previous writing in moral philosophy that relied on vague notion such as " societal well-being" and "moral duty," Binmore begins with individuals; rational decision-makers with the ability to empathize with one another. Any social arrangement that prescribes them to act against their interests will become unstable and eventually will be replaced by another, until one is found that includes worthwhile actions for all individuals involved.

Ken Binmore's previous game theory textbook, Fun and Games, carved out a significant niche in the advanced undergraduate market; it was intellectually serious and more up-to-date than its competitors, but also accessibly written. Its central thesis was that game theory allows us to understand many kinds of interactions between people, a point that Binmore amply demonstrated through a rich range of examples and applications. This replacement for the now out-of-date 1991 textbook retains the entertaining examples, but changes the organization to match how game theory courses are actually taught, making Playing for Real a more versatile text that almost all possible course designs will find easier to use, with less jumping about than before. In addition, the problem sections, already used as a reference by many teachers, have become even more clever and varied, without becoming too technical. Playing for Real will sell into advanced undergraduate courses in game theory, primarily those in economics, but also courses in the social sciences, and serve as a reference for economists.

In Game Theory and the Social Contract, Ken Binmore argues that game theory provides a systematic tool for investigating ethical matters. His reinterpretation of classical social contract ideas within a game-theoretic framework generates new insights into the fundamental questions of social philosophy. He clears the way for this ambitious endeavor by first focusing on foundational issues -- paying particular attention to the failings of recent attempts to import game -- theoretic ideas into social and political philosophy.Binmore shows how ideas drawn from the classic expositions of Harsanyi and Rawls produce a synthesis that is consistent with the modern theory of noncooperative games. In the process, he notes logical weaknesses in other analyses of social cooperation and coordination, such as those offered by Rousseau, Kant, Gauthier, and Nozick. He persuasively argues that much of the current literature elaborates a faulty analysis of an irrelevant game.Game Theory and the Social Contract makes game-theoretic ideas more widely accessible to those with only a limited knowledge of the field. Instructional material is woven into the narrative, which is illustrated with many simple examples, and the mathematical content has been reduced to a minimum.

Binmore's groundbreaking text on game theory explores the manner in which rational people should interact when they have conflicting interests. While Binmore uses a light touch to outline key developments in theory, the text remains a serious exposition of a serious topic. In addition, his unique story-telling approach allows students to immediately apply game-theoretic skills to simple problems. Each chapter ends with a host of challenging exercises to help students practice the skills they have learned. The highly anticipated revision, expected in 2003, will include more coverage of cooperative game theory and a more accessible presentation—with chapters broken up into smaller chunks and an abundance of economic examples integrated throughout the text.

For the second edition of this very successful text, Professor Binmore has written two chapters on analysis in vector spaces. The discussion extends to the notion of the derivative of a vector function as a matrix and the use of second derivatives in classifying stationary points. Some necessary concepts from linear algebra are included where appropriate. The first edition contained numerous worked examples and an ample collection of exercises for all of which solutions were provided at the end of the book. The second edition retains this feature but in addition offers a set of problems for which no solutions are given. Teachers may find this a helpful innovation.

This second edition of a text for a course on calculus of functions of several variables begins with basics of matrices and vectors and a chapter recalling the important points of the theory in one dimension. It then introduces partial derivatives via functions of two variables and then extends the discussion to more than two variables. This pattern is repeated throughout the book, with two variables being used as a springboard for the more general case. The book distinguishes itself from the competition with its introduction of elementary difference equations, including the use of the difference operator, as well as differential equations and complex numbers. It overcomes the difficulty of visualizing curves and surfaces from equations with the use of many computer graphics in full color, and it contains more than 250 exercises. With applications to economics and an emphasis on practical problem-solving in the sciences rather than the proof of formal theorems, this text should provide excellent motivation to students.

In Volume 1 of Game Theory and the Social Contract, Ken Binmore restated the problems of moral and political philosophy in the language of game theory. In Volume 2, Just Playing, he unveils his own controversial theory, which abandons the metaphysics of Immanuel Kant for the naturalistic approach to morality of David Hume. According to this viewpoint, a fairness norm is a convention that evolved to coordinate behavior on an equilibrium of a society's Game of Life. This approach allows Binmore to mount an evolutionary defense of Rawls's original position that escapes the utilitarian conclusions that follow when orthodox reasoning is applied with the traditional assumptions. Using ideas borrowed from the theory of bargaining and repeated games, Binmore is led instead to a form of egalitarianism that vindicates the intuitions that led Rawls to write his Theory of Justice. Written for an interdisciplinary audience, Just Playing offers a panoramic tour through a range of new and disturbing insights that game theory brings to anthropology, biology, economics, philosophy, and psychology. It is essential reading for anyone who thinks it likely that ethics evolved along with the human species.

A collection of Ken Binmore's influential papers on bargaining experiments, with the author's newly written commentary addressing the challenges to game theory posed by the behavioral school of economics. This volume brings together all of Ken Binmore's influential experimental papers on bargaining along with newly written commentary in which Binmore discusses the underlying game theory and addresses the criticism leveled at it by behavioral economists. When Binmore began his experimental work in the 1980s, conventional wisdom held that game theory would not work in the laboratory, but Binmore and other pioneers established that game theory can often predict the behavior of experienced players very well in favorable laboratory settings. The case of human bargaining behavior is particularly challenging for game theory. Everyone agrees that human behavior in real-life bargaining situations is governed at least partly by considerations of fairness, but what happens in a laboratory when such fairness considerations supposedly conflict with game-theoretic predictions? Behavioral economists, who emphasize the importance of other-regarding or social preferences, sometimes argue that their findings threaten traditional game theory. Binmore disputes both their interpretations of their findings and their claims about what game theorists think it reasonable to predict. Binmore's findings from two decades of game theory experiments have made a lasting contribution to economics. These papers―some co-authored with other leading economists, including Larry Samuelson, Avner Shaked, and John Sutton―show that game theory does indeed work in favorable laboratory environments, even in the challenging case of bargaining. Does Game Theory Work? The Bargaining Challenge , Volume 2

In elementary introductions to mathematical analysis, the treatment of the logical and algebraic foundations of the subject is necessarily rather skeletal. This book attempts to flesh out the bones of such treatment by providing an informal but systematic account of the foundations of mathematical analysis written at an elementary level. This book is entirely self-contained but, as indicated above, it will be of most use to university or college students who are taking, or who have taken, an introductory course in analysis. Such a course will not automatically cover all the material dealt with in this book and so particular care has been taken to present the material in a manner which makes it suitable for self-study. In a particular, there are a large number of examples and exercises and, where necessary, hints to the solutions are provided. This style of presentation, of course, will also make the book useful for those studying the subject independently of taught course.

How would Plato have responded if his student Aristotle had ever challenged his idea that our senses perceive nothing more than the shadows cast upon a wall by a true world of perfect ideals? What would Charles Darwin have said to Karl Marx about his claim that dialectical materialism is a scientific theory of evolution? How would Jean-Paul Sartre have reacted to Simone de Beauvoir’s claim that the Marquis de Sade was a philosopher worthy of serious attention? This light-hearted book proposes answers to such questions by imagining dialogues between thirty-three pairs of philosophical sages who were alive at the same time. Sometime famous sages get a much rougher handling than usual, as when Adam Smith beards Immanuel Kant in his Konigsberg den. Sometimes neglected or maligned sages get a chance to say what they really believed, as when Epicurus explains that he wasn’t epicurean. Sometimes the dialogues are about the origins of modern concepts, as when Blaise Pascal and Pierre de Fermat discuss their invention of probability, or when John Nash and John von Neumann discuss the creation of game theory. Even in these scientific cases, the intention is that the protagonists come across as fallible human beings like the rest of us, rather than the intellectual paragons of philosophical textbooks.

The Foundations of A Straightforward Introduction, Book 2: Topological Ideas

Why can't we think straight about the big issues that face our society? Why are we taken in by the phony arguments of populists and scammers? Where are the philosophers hiding when we need them to tell us what makes sense? They are hiding because they have nothing to say. The airy-fairy answers offered by writers of footnotes to Plato were wrong two thousand years ago, and they are still wrong now. All this time, we should have been listening to a different but equally venerable branch of matter-of-fact philosophy pioneered by the much-maligned philosopher Epicurus. His ideas were suppressed in ancient times as heretical, but the development of the theory of games and decisions makes it timely for those of us who care about science to revive his style of thinking–not just about the world around us but about ourselves as well. The price of transferring our allegiance to Epicurus and his modern followers is that we can no longer enjoy the luxury of being told what we want to hear. It would be nice if we were really equipped with a hotline to a metaphysical world of transcendental ideals, but the truth is that we are just the flotsam left behind on the beach when the evolutionary tide went out, and we have to get real about what will and will not work for our imperfect species before it is too late. This book is an attempt to point the way. It has no equations and very little jargon; nor does it pull any punches, either in explaining how game theory works or in exposing the follies of famous metaphysicians.

People who put the public good before their own self interest have been admired throughout history. But what is the public good? Sages and prophets who think they know better what is good for us than we know ourselves held sway on this subject for more than two thousand years. The world had to wait for the Enlightenment that burst upon the world in the eighteenth century for an account of the public good free from the prejudices of the privileged classes. Utilitarianism is our name for this new way of thinking about morality. Francis Hutcheson encapsulated its aims by inventing its catchphrase “The greatest happiness for the greatest number’’ fifty years before Jeremy Bentham, to whom the slogan is usually attributed. But what is happiness? Why did Jeremy Bentham and John Stuart Mill prefer to speak of utility? How did economists develop this notion? Does it really make sense to compare the utilities of different people? Bob may complain more than Alice in the dentist’s chair, but is he really suffering more? Why should I put the sum of everybody’s utility before my own utility? This short book asks how such questions arose from the social and political realities of the times in which the early utilitarians lived. Nobody need fear being crushed by heavy metaphysical reasoning or incomprehensible algebra when this story is told. This book argues that the answers to all the questions that the early utilitarians found so difficult are transparent when we stand upon their shoulders to look back upon their work. The problem for the early utilitarians was to free themselves from the prejudices of their time. The lesson for us is perhaps that we too need to free ourselves from the prejudices of our own time.

This book is concerned with the calculus of several variables and provides an introduction to elementary differential and difference equations. The emphasis is on practical problem-solving rather than the proof of formal theorems. Many worked examples are supplied as well as problems for the student to solve, together with their solutions. The techniques are illustrated with applications drawn chiefly from economics, statistics and operational research. Some elementary knowledge of the calculus of one variable is assumed but revision material is supplied throughout the text. A confident approach to problem-solving is not possible without some understanding of the background theory. In this book the theory is presented systematically but informally. Wherever possible, geometric arguments are used and the text is illustrated with numerous diagrams. Particular care has been taken to make the main body of the text suitable for students who are studying independently of a taught course. The book will interest students at universities and other higher education institutions. At the London School of Economics, the course on which this book is based is attended by students reading for a variety of different degrees and with a wide disparity in their previous levels of mathematical training. Some are graduates and some are first-year undergraduates. It is hoped that this book will attract a similar audience: not only of economists, statisticians and other social scientists but also physical scientists, engineers and mathematicians.

Why can't we think straight about the big issues that face our society? Why are we taken in by the phony arguments of populists and scammers? Where are the philosophers hiding when we need them to tell us what makes sense?They are hiding because they have nothing to say. The airy-fairy answers offered by writers of footnotes to Plato were wrong two thousand years ago, and they are still wrong now. All this time, we should have been listening to a different but equally venerable branch of matter-of-fact philosophy pioneered by the much-maligned philosopher Epicurus. His ideas were suppressed in ancient times as heretical, but the development of the theory of games and decisions makes it timely for those of us who care about science to revive his style of thinking–not just about the world around us but about ourselves as well. The price of transferring our allegiance to Epicurus and his modern followers is that we can no longer enjoy the luxury of being told what we want to hear. It would be nice if we were really equipped with a hotline to a metaphysical world of transcendental ideals, but the truth is that we are just the flotsam left behind on the beach when the evolutionary tide went out, and we have to get real about what will and will not work for our imperfect species before it is too late.This book is an attempt to point the way. It has no equations and very little jargon; nor does it pull any punches, either in explaining how game theory works or in exposing the follies of famous metaphysicians.

Ken Binmore's Learn Calculus Step By Step - This second edition of the course text necessary for the calculation of the functions of several variables begins with a basis of matrices and vectors, as well as a chapter recalling important aspects of the theory in one dimension. He then introduces partial derivatives through the functions of two variables and extends the discussion to more than two variables. This pattern is repeated throughout the book, using two variables as a springboard for the more general case. The book differentiates itself from the competition by introducing basic difference equations, including the use of a difference operator, as well as differential equations and complex numbers. It overcomes the difficulty of displaying curves and surfaces from an equation using many color infographics and includes over 250 exercises. By applying to economics and focusing on solving practical problems in science subjects rather than demonstrating formal theorems, this text should provide excellent motivation for students.

Book by Binmore, Ken

In recent years economists have found the theory of games to be an attractive route for exploring imperfectly competitive markets. This collection of articles explores both the potential and the limitations of this theoretical framework.

These seventeen contributions take up the most recent research in game theory, reflecting the many diverse approaches in the field today. They are classified in five general tactical categories - prediction, explanation, investigation, description, and prescription - and wit in these along applied and theoretical divisions. The introduction clearly lays out this framework.