Are people ever rational? Consider this: You auction off a one-dollar bill to the highest bidder, but you set the rules so that the second highest bidder also has to pay the amount of his last bid, even though he gets nothing. Would people ever enter such an auction? Not only do they, but according to Martin Shubik, the game's inventor, the average winning bid (for a dollar, remember) is $3.40. Many winners report that they bid so high only because their opponent "went completely crazy." This game lies at the intersection of three subjects of eternal fascination: human psychology, morality, and John von Neumann's game theory. Hungarian game-theorist Laszlo Mero introduces us to the basics of game theory, including such concepts as zero-sum games, Prisoner's Dilemma and the origins of altruism; shows how game theory is applicable to fields ranging from physics to politics; and explores the role of rational thinking in the context of many different kinds of thinking. This fascinating, urbane book will interest everyone who wonders what mathematics can tell us about the human condition.

Pólya and Szegö’s classic treatment of isoperimetric inequalities in mathematical physics from the acclaimed Annals of Mathematics Studies series Princeton University Press is proud to have published the Annals of Mathematics Studies since 1940. One of the oldest and most respected series in science publishing, it has included many of the most important and influential mathematical works of the twentieth century. The series continues this tradition as Princeton University Press publishes the major works of the twenty-first century. To mark the continued success of the series, all books are available in paperback and as ebooks.

Rapid advances in the physical and biological sciences and in related technologies have brought about equally farreaching changes in mathematical research. Focusing on control theory, invariant imbedding, dynamic programming, and quasilinearization, Mr. Bellman explores with ease and clarity the mathematical research problems arising from scientific questions in engineering, physics, biology, and medicine. Special attention is paid in these essays to the use of the digital computer in obtaining the numerical solution of numerical problems, its influence in the formulation of new and old scientific problems in new terms, and to some of the effects of the computer revolution on educational and social systems. The new opportunities for mathematical research presage, Bellman concludes, a renaissance of mathematics in human affairs by involving it closely in the problems of society.