The calculus of selfishness begins with a calculated approach towards the daily incidents an individual can experience. Completely devoid of any mathematical intricacies, borrowing heavily from real life, the first chapter summarizes and justifies the calculations, which are seen in the rest of the book. This draws the reader deeply into the plot making more curious about how mathematics can encapsulate such complex scenarios? This is exactly is what is answered in the second chapter which essentially describes the foundations of evolutionary game theory and explores its roots in traditional game theory and the concepts and terminologies are made clear.
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.