Evolution's "natural selection" is often portrayed as an "every man / organism for himself" battle. Reconciling the selective logic to favor one's own genes over other genes with cooperation (or putting oneself at risk to help others) has been an issue since Darwin. Observations show even in pre-human species cooperation is used, but doesn't necessarily tell us why. The central theme of this book is the use of mathematical modeling and simulations in order to show what kinds of selfish or cooperative strategies actually can prevail.
In the mathemeatical discipline of game theory, the Prisoner's Dilemma game has shown that acting selfishly may be a reasonable strategy when you won't have to interact with the same person in the future, but if you'll have to repeatedly interact with the same person it is a poor strategy. Initially, in computer simulations, the best strategy seemed to be to act against the other person once for every time the other person acted against you. However, it was later recognized that this isn't the best strategy for humans - because humans are imperfect. Humans sometimes mis-remember who treated them well or poorly the last time, humans may make mistakes, humans may act out of character when having a bad day. Therefore, the best strategy is to always treat someone good after they treat you good, and treat them poorly more often than not after they treat you poorly.
In computer simulations in which "individuals" using various strategies interact, they find the dominant strategy changes over time. At first, it's the selfish strategy that does best, but then increasingly cooperative strategies dominate. Eventually, an always-cooperate strategy dominates for a while. But in that situation, the selfish strategy is able to gain ground again - and the cycle repeats. [The book doesn't discuss how an organized society working to influence this might achieve. A society which was aware of these possible cycles could maintain penalties for types of selfish behavior so there wouldn't be a true "always cooperate" strategy phase.]
The next section is on indirect reciprocity and reputation. Indirect reciprocity adds an additional dimension to members of a society getting help when they need it. IF Person A helps Person B, there are fewer possibilities for Person A to get help in the future if it depends solely on Person B being able to help Person A in the way that in needed. However, Person B may have a family member or friend who is willing to return the favor to Person A. Reputation can expand this further. If people know that Person A helps others when they need it, they are more likely to help Person A when he needs it. They know Person A is the kind of person who will help them or people they care about. Helping those known to be Good Samaritans tends to maintain a society with a number of Good Samaritans, average people who have received help (and therefore are more likely to be helpful) and a sense of friendly community - all of which increase the probability that someone or other will help you when you need it. Meanwhile, if you have a reputation of not helping others, people will be less likely to help you. That reduces the survival prospects of those who never help others and might encourage those who prefer not to help others to be occassionally helpful in order to be able to get help when they need it.
[I've wondered why people are so helpful to the blind. A blind person may be less able to reciprocate, as much as he wants to. So, why don't people prefer helping non-disabled persons? Just empathy may not do it. Perhaps, when Person A helps Person B, Person A feels good about himself - he feels capable and successful. The psychology of intelligent beings makes us want to associate good outcomes with wise choices. If we can do what others can't, we think well of ourselves. Each person has strengths and weaknesses, so each person can help someone else with something. If this is a factor, it need not be blind people we're helping. There may be ways to encourage cooperation this way without over-inflating egos.]
The indirect recipocity section discusses what strategies would take into account the good and bad reputations of others and the actions we take toward them that would affect our repuations. They find this leads to a growing matrix of peossible strategies. One consideration is that Person A may have good reason not to help Person B, but if that reason isn't clear to others, Person A may get a bad reputation if he doesn't help Person B.
In the third section, the author explains that the previous strategies had been based on individuals interacting in random combinations. He explains that when simulations of cooperative and selfish strategies take place in a more structured setting or where a chessboard pattern makes some people neighbors then cooperative strategies do better.
Group selection. His model indicates that groups with cooperation do better when there are many small groups, but not so well when there are a few large groups. Migration of selfish exploiters from one cooperative group to another undermines the sucess of cooperation.
Kin selection. He says that while there seems to be some logic in cooperative help to kin and therefore helping one's own genes survive, there are issues in the mathematical modeling of this. The evidence isn't as clear, but may still be a factor.
The remainder of the book presents work the author did in areas such as how selfish / cooperative interactions within organisms can improve their evolutionary advantage, how "cooperation" or "non-cooperation" among pre-life molecules could play are role in the development of life, and the evolution of language. These topics will be of interest to some readers, but may not seem relevant to some readers who wish to focus on the role of cooperation among members of an intelligent species.
The discussion on the "evolution" of pre-life molecules may be of interest to those interested in the probability of life on other worlds, and those who have wondered why those Earth life-forms we tend to be familiar with seem to all have the same primordial ancestor - rather than there having been multiple independent "first organisms".
He discusses individual life-style choices related to climate change in terms of selfish / cooperative action. However, there's little about business choices, government regulation or the like.
The author follows his career in mathematical disciplines related to evolution, cooperation and social interactions. This includes his team building the areas of evolutionary graph theory and evolutionary set theory. It continues to add more facets to the previous understanding. Among other things, we learn that cooperation is more successful in smaller groups where individuals can expect repeated interactions with the same people and in situations where people have various potential types of connections to others which allows them to find groups where cooperation is active, and where individuals can find others with multiple commonalities on which to bond.
If I had to choose between relying on observations of the real world or mathematical simulations to determine what theory was correct, I'd choose the observations. However, having both suggest to us the usefulness of cooperation makes the case stronger.