  Cooperation lies at the foundations of human societies, yet why people
cooperate remains a conundrum. The issue, known as network reciprocity, of
whether population structure can foster cooperative behavior in social dilemmas
has been addressed by many, but theoretical studies have yielded contradictory
results so far---as the problem is very sensitive to how players adapt their
strategy. However, recent experiments with the prisoner's dilemma game played
on different networks have shown that humans do not consider neighbors' payoffs
when making their decisions, and that the network structure does not influence
the final outcome. In this work we carry out an extensive analysis of different
evolutionary dynamics for players' strategies, showing that the absence of
network reciprocity is a general feature of those dynamics that do not take
neighbors' payoffs into account. Our results, together with experimental
evidence, hint at how to properly model real people's behavior.
