title: Cooperation and control in multiplayer social dilemmas.
abstract: Direct reciprocity and conditional cooperation are important mechanisms to prevent free riding in social dilemmas. However, in large groups, these mechanisms may become ineffective because they require single individuals to have a substantial influence on their peers. However, the recent discovery of zero-determinant strategies in the iterated prisoner's dilemma suggests that we may have underestimated the degree of control that a single player can exert. Here, we develop a theory for zero-determinant strategies for iterated multiplayer social dilemmas, with any number of involved players. We distinguish several particularly interesting subclasses of strategies: fair strategies ensure that the own payoff matches the average payoff of the group; extortionate strategies allow a player to perform above average; and generous strategies let a player perform below average. We use this theory to describe strategies that sustain cooperation, including generalized variants of Tit-for-Tat and Win-Stay Lose-Shift. Moreover, we explore two models that show how individuals can further enhance their strategic options by coordinating their play with others. Our results highlight the importance of individual control and coordination to succeed in large groups.
authors.affiliation: Program for Evolutionary Dynamics, Departments of Mathematics and Organismic and Evolutionary Biology, Harvard University, Cambridge, MA 02138; and Department of Evolutionary Theory, Max Planck Institute for Evolutionary Biology, 24306 Plön, Germany hilbe@fas.harvard.edu.
authors.forename: Christian
authors.initials: C
authors.lastname: Hilbe
authors.affiliation: Department of Evolutionary Theory, Max Planck Institute for Evolutionary Biology, 24306 Plön, Germany.
authors.forename: Bin
authors.initials: B
authors.lastname: Wu
authors.affiliation: Department of Evolutionary Theory, Max Planck Institute for Evolutionary Biology, 24306 Plön, Germany.
authors.forename: Arne
authors.initials: A
authors.lastname: Traulsen
authors.affiliation: Program for Evolutionary Dynamics, Departments of Mathematics and Organismic and Evolutionary Biology, Harvard University, Cambridge, MA 02138; and.
authors.forename: Martin A
authors.initials: MA
authors.lastname: Nowak
mesh_terms: D000465:Algorithms; D003163:Competitive Behavior; D003198:Computer Simulation; D003299:Cooperative Behavior; D005717:Games, Experimental; D006126:Group Processes; D006801:Humans; D007389:Internal-External Control; D008960:Models, Psychological; D012919:Social Behavior
keywords: alliances; cooperation; evolutionary game theory; public goods game; volunteer's dilemma