This volume explores from multiple perspectives the subtle and interesting relationship between the theory of rational choice and Darwinian evolution. In rational choice theory, agents are assumed to make choices that maximize their utility; in evolution, natural selection 'chooses' between phenotypes according to the criterion of fitness maximization. So there is a parallel between utility in rational choice theory and fitness in Darwinian theory. This conceptual link between fitness and utility is mirrored by the interesting parallels between formal models of evolution and rational choice. The essays in this volume, by leading philosophers, economists, biologists and psychologists, explore the connection between evolution and rational choice in a number of different contexts, including choice under uncertainty, strategic decision making and pro-social behaviour. They will be of interest to students and researchers in philosophy of science, evolutionary biology, economics and psychology.

This book lays out foundations for a "science of morals." Binmore uses game theory as a systematic tool forassical investigating ethical matters. He reinterprets classical social contract ideas within a game-theory framework and generates new insights into the fundamental questions ofin social philosophy. In contrast to the previous writing in moral philosophy that relied on vague notion such as "with societal well-being" and "moral duty," Binmore begins with individuals; rational decision-makers with the ability to emphasize with one another. Any social arrangement thate 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.

This volume explores from multiple perspectives the subtle and interesting relationship between the theory of rational choice and Darwinian evolution. In rational choice theory, agents are assumed to make choices that maximize their utility; in evolution, natural selection 'chooses' between phenotypes according to the criterion of fitness maximization. So there is a parallel between utility in rational choice theory and fitness in Darwinian theory. This conceptual link between fitness and utility is mirrored by the interesting parallels between formal models of evolution and rational choice. The essays in this volume, by leading philosophers, economists, biologists and psychologists, explore the connection between evolution and rational choice in a number of different contexts, including choice under uncertainty, strategic decision making and pro-social behaviour. They will be of interest to students and researchers in philosophy of science, evolutionary biology, economics and psychology.

Games are everywhere: Drivers manoeuvring in heavy traffic are playing a driving game. Bargain hunters bidding on eBay are playing an auctioning game. A firm negotiating next year's wage is playing a bargaining game. The opposing candidates in an election are playing a political game. The supermarket's price for corn flakes is decided by playing an economic game. Game theory is about how to play such games in a rational way. Even when the players have not thought everything out in advance, game theory often works for the same reason that mindless animals sometimes end up behaving very cleverly: evolutionary forces eliminate irrational play because it is unfit. Game theory has seen spectacular successes in evolutionary biology and economics, and is beginning to revolutionize other disciplines from psychology to political science. This Very Short Introduction introduces the fascinating world of game theory, showing how it can be understood without mathematical equations, and revealing that everything from how to play poker optimally to the sex ratio among bees can be understood by anyone willing to think seriously about the problem. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.

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.

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.

Ken Binmore's previous game theory textbook, Fun and Games (D.C. Heath, 1991), 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.

Binmore argues that game theory provides a systematic tool for investigating ethical matters. 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.

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.

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 emphasize 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.

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.