Calculus of Selfishness

Karl Sigmund is professor of mathematics at the University of Vienna. He is the author of Games of Life (Penguin), coauthor of Evolutionary Games and Population Dynamics, and a contributor to Nature and Science.

• Preface vii Chapter 1: Introduction: Social Traps and Simple Games 1 Chapter 2: Game Dynamics and Social Learning 25 Chapter 3: Direct Reciprocity: The Role of Repetition 49 Chapter 4: Indirect Reciprocity: The Role of Reputation 82 Chapter 5: Fairness and Trust: The Power of Incentives 104 Chapter 6: Public Goods and Joint Efforts: Between Freedom and Enforcement 123 Chapter 7: Cooperation in Structured Populations 145 References 155 Index 169

"With collaborators from Vienna, Sigmund has pioneered the development of evolutionary game dynamics. This thought-provoking book is a distillation of his many influential contributions to the field. It is a showcase of clever models and elegant mathematics, replete with sometimes counterintuitive insights."--Nature "In The Calculus of Selfishness, Karl Sigmund provides a comprehensive and accessible mathematical exposition of the evolutionary game theory of selfishness. The book should prove accessible to natural and social scientists as its mathematical arguments employ intuition, geometry, and simulation with a minimum of axiomatic formality. The demands on the reader typically involve little more than linear algebra and calculus."--David Krakauer, Science "Sigmund's mathematical exposition is exemplary. He starts with the presumption that the reader has only rudimentary linear algebra and some notion of what a differential equation is, and he builds up from there, introducing more advanced concepts and results as needed. He avoids formal proofs and bookkeeping in favor of careful explanations of key points and illustrative calculations. As he teaches evolutionary game theory, Sigmund is also demonstrating how to write about applied mathematics."--Cosma Shalizi, American Scientist "Sigmund's writing is admirably clear and historically grounded and he wisely restricts his coverage primarily to a subset of situations... [Sigmund] makes fascinating reading for the interested general reader and provides a good background in game theory which should inoculate readers from being fooled by sloppy or completely incorrect references in the popular media."--Sarah Boslaugh, MAA Reviews "Sigmund has ... done an admirable job of motivating the material and making it accessible for the non-expert who is interested in theories to explain the evolution of cooperation."--Ross Cressman, Mathematical Reviews