The emergence and stability of cooperative behavior is a fundamental open problem in economics and sociology, and evolutionary game theory has proven to be one of the most fruitful approaches to study it. The seminal work by Nowak and May [1] showed that if agents interact according to a given network of relationships, i.e. a population structure, cooperation is greatly enforced. Since then, a great number of works have exploited this idea [2], considering different games, population structures and rules for the updating of strategies, reporting a promotion of cooperation in some cases [3] and an inhibition in others [4,5]. The current situation is that there is not a precise and general understanding of the effect of population structure on evolutionary cooperative games. More importantly, neither the basic topological properties nor the resultant dynamic mechanisms that affect cooperation have been correctly identified. To address this issue, we have performed a systematic and exhaustive computational study of the evolutionary models based on 2x2 symmetric games. This has allowed us to isolate the effect of each kind of population structure in the different configurations of games and update rules. We have found that population clustering (agent cliquishness) and degree heterogeneity (variance in the number of relationships of each agent) are the key topological properties that condition cooperation, as well as the underlying mechanisms that take place in both cases. Additionally, we definitely clarify the effect that these topological properties have on each kind of game, and how this effect is strongly influenced by the particular update rule used.

[1] M.A. Nowak and R.M. May, Nature 359, 826 (1992)
[2] G. Szabó and G. Fáth, Physics Reports 446, 97 (2007)
[3] F.C. Santos et al, PNAS 103, 3490 (2006)
[4] C. Hauert and M. Doebeli, Nature 428, 643 (2004)
[5] M. Sysi-Aho et al, Eur. Phys. J. B 44, 129 (2005)

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