Five Rules for the Evolution of Cooperation
http://science.sciencemag.org/content/314/5805/1560
The concepts of Evolutionarily Stable Strategy and Nash Equilibrium are introduced in class, explaining how a behavior survives in relation to its fitness. However, neither of these two theories illustrates how cooperative behavior can exist under certain circumstances. If natural selection implies competition and thus opposes cooperation, how could cooperation happen? Martin Nowak proposed five mechanisms for the evolution of cooperation a decade ago. For each mechanism, a simple rule is derived to specify whether natural selection can lead to cooperation.
The first mechanism is “Kin Selection”. The idea is that natural selection can favor cooperation if the donor and recipient of an act are genetic relatives. For example, if we are playing the prisoner dilemma with our parents or children, we tend not to betray but to cooperate. This mechanism was later known as Hamilton’s rule, which states that “the coefficient of relatedness, r, must exceed the cost-to-benefit ratio of the altruistic act to allow cooperation”. The second mechanism is called “Direct Reciprocity”, which involves repeated encounters between individuals. This framework is known as the repeated Prisoner’s Dilemma, with a “winning strategy” of “tit-for-tat”: If I cooperate now, you may cooperate later. Direct reciprocity can lead to cooperation only if “the probability, w, of another encounter between the same two individuals exceeds the cost-to-benefit ratio of the act”. The third closely related mechanism “Indirect Reciprocity” is also important. The motivation behind indirect reciprocity is reputation. We will be rewarded by others if we establish good reputations by helping others. As a result, we take into account the possible consequence for our reputation when considering whether to cooperate. Indirect reciprocity can promote cooperation if “the probability,q, of knowing someone’s reputation exceeds the cost-to-benefit ratio of the act”. Another mechanism is “Network Reciprocity”. In this case, spatial structures or social networks affect evolutionary dynamics. In social networks, the edges determine interactions and nodes form network clusters to help each other. Network reciprocity can favor cooperation if “the benefit-to-cost ratio exceeds the average number of neighbors, k, per individual”. The last one is “Group Selection”. A simple model of group selection works as follows. A population is subdivided into groups; cooperators help others in their own group, while defectors do not. After offspring are added to the same group, a group can split into two if it reaches a certain size. Another group becomes extinct in order to constrain the total population size. Therefore, if n is the maximum group size and m is the number of groups, then group selection allows evolution of cooperation if the benefit-to-cost ratio exceeds 1+ n/m.