--- _id: '671' abstract: - lang: eng text: Humans routinely use conditionally cooperative strategies when interacting in repeated social dilemmas. They are more likely to cooperate if others cooperated before, and are ready to retaliate if others defected. To capture the emergence of reciprocity, most previous models consider subjects who can only choose from a restricted set of representative strategies, or who react to the outcome of the very last round only. As players memorize more rounds, the dimension of the strategy space increases exponentially. This increasing computational complexity renders simulations for individuals with higher cognitive abilities infeasible, especially if multiplayer interactions are taken into account. Here, we take an axiomatic approach instead. We propose several properties that a robust cooperative strategy for a repeated multiplayer dilemma should have. These properties naturally lead to a unique class of cooperative strategies, which contains the classical Win-Stay Lose-Shift rule as a special case. A comprehensive numerical analysis for the prisoner's dilemma and for the public goods game suggests that strategies of this class readily evolve across various memory-n spaces. Our results reveal that successful strategies depend not only on how cooperative others were in the past but also on the respective context of cooperation. article_processing_charge: Yes (in subscription journal) author: - first_name: Christian full_name: Hilbe, Christian id: 2FDF8F3C-F248-11E8-B48F-1D18A9856A87 last_name: Hilbe orcid: 0000-0001-5116-955X - first_name: Vaquero full_name: Martinez, Vaquero last_name: Martinez - first_name: Krishnendu full_name: Chatterjee, Krishnendu id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87 last_name: Chatterjee orcid: 0000-0002-4561-241X - first_name: Martin full_name: Nowak, Martin last_name: Nowak citation: ama: Hilbe C, Martinez V, Chatterjee K, Nowak M. Memory-n strategies of direct reciprocity. PNAS. 2017;114(18):4715-4720. doi:10.1073/pnas.1621239114 apa: Hilbe, C., Martinez, V., Chatterjee, K., & Nowak, M. (2017). Memory-n strategies of direct reciprocity. PNAS. National Academy of Sciences. https://doi.org/10.1073/pnas.1621239114 chicago: Hilbe, Christian, Vaquero Martinez, Krishnendu Chatterjee, and Martin Nowak. “Memory-n Strategies of Direct Reciprocity.” PNAS. National Academy of Sciences, 2017. https://doi.org/10.1073/pnas.1621239114. ieee: C. Hilbe, V. Martinez, K. Chatterjee, and M. Nowak, “Memory-n strategies of direct reciprocity,” PNAS, vol. 114, no. 18. National Academy of Sciences, pp. 4715–4720, 2017. ista: Hilbe C, Martinez V, Chatterjee K, Nowak M. 2017. Memory-n strategies of direct reciprocity. PNAS. 114(18), 4715–4720. mla: Hilbe, Christian, et al. “Memory-n Strategies of Direct Reciprocity.” PNAS, vol. 114, no. 18, National Academy of Sciences, 2017, pp. 4715–20, doi:10.1073/pnas.1621239114. short: C. Hilbe, V. Martinez, K. Chatterjee, M. Nowak, PNAS 114 (2017) 4715–4720. date_created: 2018-12-11T11:47:50Z date_published: 2017-05-02T00:00:00Z date_updated: 2021-01-12T08:08:37Z day: '02' department: - _id: KrCh doi: 10.1073/pnas.1621239114 ec_funded: 1 external_id: pmid: - '28420786' intvolume: ' 114' issue: '18' language: - iso: eng main_file_link: - open_access: '1' url: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5422766/ month: '05' oa: 1 oa_version: Published Version page: 4715 - 4720 pmid: 1 project: - _id: 2581B60A-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '279307' name: 'Quantitative Graph Games: Theory and Applications' - _id: 2584A770-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P 23499-N23 name: Modern Graph Algorithmic Techniques in Formal Verification - _id: 25863FF4-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: S11407 name: Game Theory publication: PNAS publication_identifier: issn: - '00278424' publication_status: published publisher: National Academy of Sciences publist_id: '7053' quality_controlled: '1' scopus_import: 1 status: public title: Memory-n strategies of direct reciprocity type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 114 year: '2017' ...