{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,7,29]],"date-time":"2024-07-29T16:33:30Z","timestamp":1722270810062},"reference-count":34,"publisher":"MIT Press","issue":"2","license":[{"start":{"date-parts":[[2022,8,26]],"date-time":"2022-08-26T00:00:00Z","timestamp":1661472000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["direct.mit.edu"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2023,5,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>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\u00e9vy flight. A L\u00e9vy flight is a kind of random walk but it is composed of many small movements with a few big movements. The role of L\u00e9vy flights for cooperation has been studied by Antonioni and Tomassini, who showed that L\u00e9vy flights promoted cooperation combined with conditional movements triggered by neighboring defectors. However, the optimal condition for neighboring defectors and how the condition changes with the intensity of L\u00e9vy flights are still unclear. Here, we developed an agent-based model in a square lattice where agents perform L\u00e9vy flights depending on the fraction of neighboring defectors. We systematically studied the relationships among three factors for cooperation: sensitivity to defectors, the intensity of L\u00e9vy flights, and population density. Results of evolutionary simulations showed that moderate sensitivity most promoted cooperation. Then, we found that the shortest movements were best for cooperation when the sensitivity to defectors was high. In contrast, when the sensitivity was low, longer movements were best for cooperation. Thus, L\u00e9vy flights, the balance between short and long jumps, promoted cooperation in any sensitivity, which was confirmed by evolutionary simulations. Finally, as the population density became larger, higher sensitivity was more beneficial for cooperation to evolve. Our study highlights that L\u00e9vy flights are an optimal searching strategy not only for foraging but also for constructing cooperative relationships with others.<\/jats:p>","DOI":"10.1162\/artl_a_00382","type":"journal-article","created":{"date-parts":[[2022,8,26]],"date-time":"2022-08-26T16:35:48Z","timestamp":1661531748000},"page":"187-197","update-policy":"http:\/\/dx.doi.org\/10.1162\/mitpressjournals.corrections.policy","source":"Crossref","is-referenced-by-count":1,"title":["How L\u00e9vy Flights Triggered by the Presence of Defectors Affect Evolution of Cooperation in Spatial Games"],"prefix":"10.1162","volume":"29","author":[{"given":"Genki","family":"Ichinose","sequence":"first","affiliation":[{"name":"Shizuoka University, Department of Mathematical and Systems Engineering. ichinose.genki@shizuoka.ac.jp"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Daiki","family":"Miyagawa","sequence":"additional","affiliation":[{"name":"Shizuoka University, Department 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