- Series: Princeton Series in Theoretical and Computational Biology
- Hardcover: 184 pages
- Publisher: Princeton University Press; Edition Unstated edition (January 24, 2010)
- Language: English
- ISBN-10: 0691142750
- ISBN-13: 978-0691142753
- Product Dimensions: 6.1 x 0.7 x 9.3 inches
- Shipping Weight: 13 ounces (View shipping rates and policies)
- Average Customer Review: 4 customer reviews
- Amazon Best Sellers Rank: #2,498,858 in Books (See Top 100 in Books)
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The Calculus of Selfishness (Princeton Series in Theoretical and Computational Biology) Edition Unstated Edition
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"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
From the Back Cover
"Karl Sigmund helped conceive the field of evolutionary game theory and has dominated it for over thirty years. With The Calculus of Selfishness, he has written a highly engaging and captivating book for students and experts who want to learn about one of the most fascinating fields of science. When it comes to Karl Sigmund we are all students. This book is written for you and me."--Martin Nowak, Harvard University
"In this outstanding and beautiful book, Karl Sigmund extends the theory of games to understand how variations in real social situations alter social outcomes. With elegance, he clarifies the results from different studies, fully develops the concepts of reputation and trust, and gives the foundations for moving the discipline to the next level."--Steven Frank, University of California, Irvine
Top customer reviews
The chapters after that make clear the title of the book. Exploring the effects (or the cause?) of direct and indirect reciprocity, models involving reputation, rewards and punishment are analyzed for the evolution and maintenance of cooperation. Lastly how collective actions are sustained and maintained is theorized, again involving the above-mentioned subjects. The role of structured populations is touched upon briefly but not without presenting the important results which have been popularized until now.
In a nutshell, Karl Sigmund shows us again what makes him an authority in the field of evolutionary game dynamics and puts together the most important concepts which have been developed in this field since its inception. His earlier book "Games of Life" generated interest in many a physicists and mathematicians in biology and made biologists look towards biology through the looking glass of the mathematics of dynamical systems creating a generation of evolutionary dynamicists. It wouldn't be surprising if this one did the same and more.
Enter Karl Sigmund, an accomplished mathematician with a serious love affair for the evolutionary modeling of social life, as witnessed by his previous contribution, Games of Life (Penguin Books, 1995). Sigmund develops classical game theory as well as the evolutionary game theory that takes a classical game as its stage game, which it embeds in a population structure such that sets of agents meet in each period and play the stage game. Periodically, more successful agents reproduce and less successful agents die off, as in a Darwinian dynamic. The result analytically is called a monotonic dynamic, of which the replicator dynamic is the most famous and commonly used example. There are many elegant properties of evolutionary games of this type (see my textbook on the subject, Game Theory Evolving, Princeton, 2009), but Sigmund sticks to models that can be modeled two-dimensionally, usually using barycentric coordinates, so generally the models allow agents to have three different pure strategies.
This book is well-suited for teaching or self-learning. While Sigmund touches upon a variety of games, most of the material is devoted to two-player social dilemma games, the Prisoner's Dilemma (PD) game in some form being most intensively studied. The central point is that in such games selfish players will never cooperate, but if the social setting is properly structured, they may cooperate.
Sigmund devotes a chapter to direct reciprocity, which is called reciprocal altruism in the biological literature (Trivers, 1971) and tit-for-tat in the economic literature (Axelrod 1984). This leads him to deal with repeated games, stressing the role of errors in compromising efficiency. Sigmund then devotes a chapter to indirect reciprocity, which was proposed by the biologist Richard Alexander (1987) as an obvious extension of direct reciprocity. In an indirect reciprocity model, individuals develop reputations for good behavior that is common knowledge to all players. Players then cooperate with each other in the PD game, provided both are in `good standing.' Moreover, a player who defects on a another player who is in `good standing'' moves to being in `bad standing.' A high level of cooperation can be sustained in such a model, but it is rather unrealistic to assume in most situations that reputations will be accurate enough to render cooperation an individual best response, especially when the error rate is not very low, or the condition of cooperating is private information of the two players. There is little evidence of either direct or indirect reciprocity in non-human creatures (Stephens, McLinn, and Stevens 2002), but considerable evidence in humans.
Sigmund then devotes a chapter to what is known as the Trust Game. This is a sequential PD game, where the first player cooperates by giving money to the experimenter, who doubles it and sends the money to the second player. The second player can then send money back to the first player. This game differs from the standard PD game only in that one player's decision is conveyed to the second player before the latter has to decide what to do, and this rule is known to both players.
In his brief foray into many-player games, Sigmund studies the Public Goods (PG) game, stressing the research of himself and his colleagues (Hauert, Demonte, Hofbauer, and Sigmund 2002, Hauert, Haiden, and Sigmund 2004). This work is very elegant mathematically, but is rather a waste of time from a scientific standpoint because the conclusion is that when cooperation is sustained in their model, there is no material payoff to cooperation---individuals who act alone have equal payoffs with actors who cooperate in groups.
Sigmund finishes off The Calculus of Selfishness with an elegant chapter on kinship selection models on grids. As it turns out, it is relatively easy to generate cooperation on a spatial grid even without kinship, so long as agents are forced to remain near one another for an extended period of time. Essentially, PD games on a grid are simple extensions of tit-for-tat, which is relatively powerful in fostering cooperation.
The reader might wonder what is behind the title of this book. Sigmund stresses ``selfishness'' because his well aware that a huge volume of empirical results from behavioral game theory over the past two decades show that both in the laboratory and in the field, human subjects sustain cooperation not through being selfish, but rather through exhibiting other-regarding preferences and favoring such character virtues as honesty and trustworthiness (see Gintis, Bounds of Reason, 2009). Sigmund wants to make the point that much cooperation in PG and PD games can be sustained without the need for such prosocial preferences. He does show this for PD games when there is sufficient information accuracy and publicity, but not otherwise. Indeed, even in small groups, the PG game does not sustain cooperation under plausible conditions without other-regarding preferences. If humans were truly selfish, they would not have had anything close to the evolutionary success they have enjoyed (see Bowles and Gintis, A Cooperative Species, 2011)./