Memory-n strategies of direct reciprocity Journal Article

Author(s): Hilbe, Christian; Martinez, Vaquero L; Chatterjee, Krishnendu; Nowak, Martin A
Article Title: Memory-n strategies of direct reciprocity
Affiliation IST Austria
Abstract: 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.
Keywords: Evolutionary game theory; Repeated games; reciprocity
Journal Title: PNAS
Volume: 114
Issue 18
ISSN: 1091-6490
Publisher: National Academy of Sciences  
Date Published: 2017-05-02
Start Page: 4715
End Page: 4720
DOI: 10.1073/pnas.1621239114
Notes: This work was supported by the European Research Council Start Grant 279307: Graph Games (to K.C.), Austrian Science Fund (FWF) Grant P23499-N23 (to K.C.), FWF Nationale Forschungsnetzwerke Grant S11407-N23 Rigorous Systems Engineering/Systematic Methods in Systems Engineering (to K.C.), Office of Naval Research Grant N00014-16-1- 2914 (to M.A.N.), and the John Templeton Foundation (M.A.N.). The Program for Evolutionary Dynamics is supported, in part, by a gift from B. Wu and Eric Larson. C.H. acknowledges generous support from the ISTFELLOW program, and L.A.M.-V. gratefully acknowledges support from the European Research Consortium for Informatics and Mathematics Alain Bensoussan Fellowship Program.
Open access: yes (repository)