| Resumo: |
Natural selection is often regarded as a result of severe competition. Defect seems beneficial for a single individual in many cases.However, cooperation is observed in many levels of biological systems ranging from single cells to animals, including human society. We have yet known that in unstructured populations, evolution favors defectors over cooperators. On the other hand, there have been much interest on evolutionary games^1,2^ on structured population and on graphs^3-16^. Structures of biological systems and societies of animals can be taken as networks. They discover that network structures determine results of the games. Together with the recent interest of complex networks^17,18^, many researchers investigate real network structures. Recently even economists study firms' transactions structure^19^. Seminal work^11^ derives the condition of favoring cooperation for evolutionary games on networks, that is, benefit divided by cost, _b/c_, exceeds average degree, (_k_). Although this condition has been believed so far^20^, we find the condition is _b/c_ (_k~nm~_) instead. _k~nm~_ is the mean nearest neighbor degree. Our condition enables us to compare how network structure enhances cooperation across different kinds of networks. Regular network favors most, scale free network least. On ideal scale free networks, cooperation is unfeasible. We could say that (_k_) is the degree of itself, while _k~nm~_ is that of others. One of the most interesting points in network theory is that results depend not only on itself but also on others. In evolutionary games on network, we find the same characteristic.
|
