Mobility is a general feature of human and animal populations living in physical space. In particular, it has been observed that often these movements are of the Lévy flight type. In this paper we study the effect of such power-law distributed displacements on the evolution of cooperation in simple games played on diluted two-dimensional grids. Using numerical simulations, our results show that unconditional Lévy flights do not favor the evolution of cooperation. However, when Lévy jumps are performed as a reaction to a growing number of defectors in an individual׳s neighborhood, all games studied here, including the harder Prisoner׳s Dilemma, remarkably benefit from this simple heuristics and cooperation can evolve in the population.