Cooperation in scale-free networks has proven to be very robust against removal of randomly selected nodes (error) but highly sensitive to removal of the most connected nodes (attack). In this paper we analyze two comparable types of node removal in which the removal selection is based on tournaments where the fittest (raids) or the least fit (battles) nodes are chosen. We associate the two removals to two types of Maya warfare offences during the Classic period. During this period of at least 500 years, political leaders were able to sustain social order in spite of attack-like offences to their social networks. We present a computational model with a population fluctuation mechanism that operates under an evolutionary game theoretic approach using the Prisoner's Dilemma as a metaphor of cooperation. We find that paradoxically battles are able to uphold cooperation under moderate levels of raids, although raids do have a strong impact on the network structure. We infer that cooperation does not depend as much on the structure as it does on the underlying mechanism that allows the network to readjust. We relate the results to the Maya Classic period, concluding that Mayan warfare by itself cannot entirely explain the Maya political collapse without appealing to other factors that increased the pressures against cooperation.