How L\'evy flights triggered by presence of defectors affect evolution of cooperation in spatial games.

Cooperation among individuals has been key to sustaining societies. However, natural selection favors defection over cooperation. Cooperation can be favored when the mobility of individuals allows cooperators to form a cluster (or group). Mobility patterns of animals sometimes follow a L\'evy flight. A L\'evy flight is a kind of random walk but it is composed of many small movements with a few big movements. Here, we developed an agent-based model in a square lattice where agents perform L\'evy flights depending on the fraction of neighboring defectors. For comparison, we also tested normal-type movements implemented by a uniform distribution. We focus on how the sensitivity to defectors when performing L\'evy flights promotes the evolution of cooperation. Results of evolutionary simulations showed that L\'evy flights outperformed normal movements for cooperation in all sensitivities. In L\'evy flights, cooperation was most promoted when the sensitivity to defectors was moderate. Finally, as the population density became larger, higher sensitivity was more beneficial for cooperation to evolve.