title: Evolving synergetic interactions.
abstract: Cooperators forgo their own interests to benefit others. This reduces their fitness and thus cooperators are not likely to spread based on natural selection. Nonetheless, cooperation is widespread on every level of biological organization ranging from bacterial communities to human society. Mathematical models can help to explain under which circumstances cooperation evolves. Evolutionary game theory is a powerful mathematical tool to depict the interactions between cooperators and defectors. Classical models typically involve either pairwise interactions between individuals or a linear superposition of these interactions. For interactions within groups, however, synergetic effects may arise: their outcome is not just the sum of its parts. This is because the payoffs via a single group interaction can be different from the sum of any collection of two-player interactions. Assuming that all interactions start from pairs, how can such synergetic multiplayer games emerge from simpler pairwise interactions? Here, we present a mathematical model that captures the transition from pairwise interactions to synergetic multiplayer ones. We assume that different social groups have different breaking rates. We show that non-uniform breaking rates do foster the emergence of synergy, even though individuals always interact in pairs. Our work sheds new light on the mechanisms underlying such synergetic interactions.
authors.affiliation: Department of Evolutionary Theory, Max Planck Institute for Evolutionary Biology, August-Thienemann-Straße 2, 24306 Plön, Germany School of Sciences, Beijing University of Posts and Telecommunications, Beijing 100876, People's Republic of China bin.wu@evolbio.mpg.de.
authors.forename: Bin
authors.initials: B
authors.lastname: Wu
authors.affiliation: Department of Evolutionary Theory, Max Planck Institute for Evolutionary Biology, August-Thienemann-Straße 2, 24306 Plön, Germany.
authors.forename: Jordi
authors.initials: J
authors.lastname: Arranz
authors.affiliation: Liaoning Key Laboratory of Manufacturing Systems and Logistics, Institute of Industrial Engineering and Logistics Optimization, Northeastern University, Shenyang 110819, People's Republic of China Center for Systems and Control, College of Engineering, Peking University, Beijing 100871, People's Republic of China.
authors.forename: Jinming
authors.initials: J
authors.lastname: Du
authors.affiliation: School of Mathematical Sciences, Xiamen University, Xiamen 361005, People's Republic of China.
authors.forename: Da
authors.initials: D
authors.lastname: Zhou
authors.affiliation: Department of Evolutionary Theory, Max Planck Institute for Evolutionary Biology, August-Thienemann-Straße 2, 24306 Plön, Germany.
authors.forename: Arne
authors.initials: A
authors.lastname: Traulsen
mesh_terms: D001419:Bacteria; D018407:Bacterial Physiological Phenomena; D005716:Game Theory; D059013:Microbial Consortia / Q000502:physiology*; D008954:Models, Biological
keywords: cooperation; multiplayer games; synergetic interactions