title: Comparing reactive and memory-one strategies of direct reciprocity.
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.
authors.affiliation: Department of Physics, Pukyong National University, Busan 48513, Korea.
authors.forename: Seung Ki
authors.initials: SK
authors.lastname: Baek
authors.affiliation: Department of Physics and Astronomy, Sejong University, Seoul 05006, Korea.
authors.forename: Hyeong-Chai
authors.initials: HC
authors.lastname: Jeong
authors.affiliation: IST Austria, Am Campus 1, 3400 Klosterneuburg, Austria.|Program for Evolutionary Dynamics, Department of Mathematics, Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA 02138, United States of America.
authors.forename: Christian
authors.initials: C
authors.lastname: Hilbe
authors.affiliation: Program for Evolutionary Dynamics, Department of Mathematics, Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA 02138, United States of America.
authors.forename: Martin A
authors.initials: MA
authors.lastname: Nowak
mesh_terms: D000465:Algorithms; D003299:Cooperative Behavior; D005716:Game Theory; D006801:Humans; D007398:Interpersonal Relations; D008568:Memory / Q000502:physiology*; D008960:Models, Psychological; D013269:Stochastic Processes