Comparing reactive and memory-one strategies of direct reciprocity Journal Article


Author(s): Baek, Seung Ki; Jeong, Hyeongchai; Hilbe, Christian; Nowak, Martin A
Article Title: Comparing reactive and memory-one strategies of direct reciprocity
Affiliation IST Austria
Abstract: Direct reciprocity is a mechanism for the evolution of cooperation based on repeated interactions. When individuals meet repeatedly, they can use conditional strategies to enforce cooperative outcomes that would not be feasible in one-shot social dilemmas. Direct reciprocity requires that individuals keep track of their past interactions and find the right response. However, there are natural bounds on strategic complexity: Humans find it difficult to remember past interactions accurately, especially over long timespans. Given these limitations, it is natural to ask how complex strategies need to be for cooperation to evolve. Here, we study stochastic evolutionary game dynamics in finite populations to systematically compare the evolutionary performance of reactive strategies, which only respond to the co-player's previous move, and memory-one strategies, which take into account the own and the co-player's previous move. In both cases, we compare deterministic strategy and stochastic strategy spaces. For reactive strategies and small costs, we find that stochasticity benefits cooperation, because it allows for generous-tit-for-tat. For memory one strategies and small costs, we find that stochasticity does not increase the propensity for cooperation, because the deterministic rule of win-stay, lose-shift works best. For memory one strategies and large costs, however, stochasticity can augment cooperation.
Keywords: social evolution; Statistical physics
Journal Title: Scientific Reports
Volume: 6
ISSN: 20452322
Publisher: Nature Publishing Group  
Date Published: 2016-05-10
Start Page: Article number: 25676
Copyright Statement: CC BY 4.0
URL:
DOI: 10.1038/srep25676
Notes: S.K.B. gratefully acknowledge discussions with Su Do Yi. S.K.B. was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT and Future Planning (NRF-2014R1A1A1003304). H.C.J. was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2015R1D1A1A01058317). C.H. acknowledges generous funding from the Schrödinger scholarship of the Austrian Science Fund (FWF), J3475.
Open access: yes (OA journal)