title: Evolutionary Games of Multiplayer Cooperation on Graphs.
abstract: There has been much interest in studying evolutionary games in structured populations, often modeled as graphs. However, most analytical results so far have only been obtained for two-player or linear games, while the study of more complex multiplayer games has been usually tackled by computer simulations. Here we investigate evolutionary multiplayer games on graphs updated with a Moran death-Birth process. For cycles, we obtain an exact analytical condition for cooperation to be favored by natural selection, given in terms of the payoffs of the game and a set of structure coefficients. For regular graphs of degree three and larger, we estimate this condition using a combination of pair approximation and diffusion approximation. For a large class of cooperation games, our approximations suggest that graph-structured populations are stronger promoters of cooperation than populations lacking spatial structure. Computer simulations validate our analytical approximations for random regular graphs and cycles, but show systematic differences for graphs with many loops such as lattices. In particular, our simulation results show that these kinds of graphs can even lead to more stringent conditions for the evolution of cooperation than well-mixed populations. Overall, we provide evidence suggesting that the complexity arising from many-player interactions and spatial structure can be captured by pair approximation in the case of random graphs, but that it need to be handled with care for graphs with high clustering.
authors: Department of Evolutionary Theory, Max Planck Institute for Evolutionary Biology, Plön, Germany.
authors: Jorge
authors: 0000-0002-4137-1823
authors: J
authors: Peña
authors: Department of Evolutionary Theory, Max Planck Institute for Evolutionary Biology, Plön, Germany.|School of Sciences, Beijing University of Posts and Telecommunications, Beijing, China.
authors: Bin
authors: B
authors: Wu
authors: Department of Evolutionary Theory, Max Planck Institute for Evolutionary Biology, Plön, Germany.
authors: Jordi
authors: J
authors: Arranz
authors: Department of Evolutionary Theory, Max Planck Institute for Evolutionary Biology, Plön, Germany.
authors: Arne
authors: A
authors: Traulsen
mesh_terms: D005075:Biological Evolution; D019295:Computational Biology; D003198:Computer Simulation; D003299:Cooperative Behavior; D005716:Game Theory; D006801:Humans