This paper is based on the intuition of Dragonetti, an old Neapolitan economist, which argues that a society experiences economic and civic development if agents promote values and virtues, more than solely rely on punishments stated by law. We thus study the evolution of cooperative behaviors using a mechanism of endogenous social rewards for cooperation (SRC). These additional (material) rewards depend on the recognition that the society--each agent in the society--gives to cooperative strategies. We formalize it with a cultural evolution model in which the payoff matrix and the population shares coevolve. We find that this endogenous mechanism can produce a large variety of long-run situations (victory of cooperators, of non-cooperators or, finally, their coexistence) depending on the social features. Moreover, we analyze the differences between SRC and exogenous punishment, changes in cooperation costs or changes in repetition of interactions and we disentangle their respective contributions.