scholarly journals Emergence of cooperation in public goods games

2009 ◽  
Vol 276 (1660) ◽  
pp. 1379-1384 ◽  
Author(s):  
Shun Kurokawa ◽  
Yasuo Ihara
Keyword(s):  
Natural Selection ◽  
Public Goods ◽  
Group Size ◽  
Evolutionary Biology ◽  
Basin Of Attraction ◽  
Simple Expression ◽  
Evolution Of Cooperation ◽  
Emergence Of Cooperation ◽  
Third Law ◽  
The One

Evolution of cooperation has been a major issue in evolutionary biology. Cooperation is observed not only in dyadic interactions, but also in social interactions involving more than two individuals. It has been argued that direct reciprocity cannot explain the emergence of cooperation in large groups because the basin of attraction for the ‘cooperative’ equilibrium state shrinks rapidly as the group size increases. However, this argument is based on the analysis of models that consider the deterministic process. More recently, stochastic models of two-player games have been developed and the conditions for natural selection to favour the emergence of cooperation in finite populations have been specified. These conditions have been given as a mathematically simple expression, which is called the one-third law. In this paper, we investigate a stochastic model of n -player games and show that natural selection can favour a reciprocator replacing a population of defectors in the n -player repeated Prisoner's Dilemma game. We also derive a generalized version of the one-third law (the {2/[ n ( n +1)]} 1/( n −1) law). Additionally, contrary to previous studies, the model suggests that the evolution of cooperation in public goods game can be facilitated by larger group size under certain conditions.

scholarly journals Group size effects in social evolution

2018 ◽  
Author(s):  
Jorge Peña ◽  
Georg Nöldeke
Keyword(s):  
Group Size ◽  
Size Effects ◽  
Evolutionary Biology ◽  
Social Evolution ◽  
Evolutionary Dynamics ◽  
Replicator Dynamics ◽  
Basin Of Attraction ◽  
Evolution Of Cooperation ◽  
Positive Effects ◽  
Public Goods Games

AbstractHow the size of social groups affects the evolution of cooperative behaviors is a classic question in evolutionary biology. Here we investigate group size effects in the evolutionary dynamics of games in which individuals choose whether to cooperate or defect and payoffs do not depend directly on the size of the group. We find that increasing the group size decreases the proportion of cooperators at both stable and unstable rest points of the replicator dynamics. This implies that larger group sizes can have negative effects (by reducing the amount of cooperation at stable polymorphisms) and positive effects (by enlarging the basin of attraction of more cooperative outcomes) on the evolution of cooperation. These two effects can be simultaneously present in games whose evolutionary dynamics feature both stable and unstable rest points, such as public goods games with participation thresholds. Our theory recovers and generalizes previous results and is applicable to a broad variety of social interactions that have been studied in the literature.

scholarly journals Nonlinear trade-offs allow the cooperation game to evolve from Prisoner's Dilemma to Snowdrift

2017 ◽  
Vol 284 (1854) ◽  
pp. 20170228 ◽  
Author(s):  
Lin Chao ◽  
Santiago F. Elena
Keyword(s):  
Public Goods ◽  
Group Size ◽  
Prisoner's Dilemma ◽  
Prisoner’S Dilemma ◽  
Evolution Of Cooperation ◽  
Gene Products ◽  
Trade Off ◽  
Defective Interfering Particles ◽  
Trade Offs ◽  
High Level

The existence of cooperation, or the production of public goods, is an evolutionary problem. Cooperation is not favoured because the Prisoner's Dilemma (PD) game drives cooperators to extinction. We have re-analysed this problem by using RNA viruses to motivate a model for the evolution of cooperation. Gene products are the public goods and group size is the number of virions co-infecting the same host cell. Our results show that if the trade-off between replication and production of gene products is linear, PD is observed. However, if the trade-off is nonlinear, the viruses evolve into separate lineages of ultra-defectors and ultra-cooperators as group size is increased. The nonlinearity was justified by the existence of real viral ultra-defectors, known as defective interfering particles, which gain a nonlinear advantage by being smaller. The evolution of ultra-defectors and ultra-cooperators creates the Snowdrift game, which promotes high-level production of public goods.

scholarly journals Spatial dilemmas of diffusible public goods

eLife ◽  
2013 ◽  
Vol 2 ◽  
Author(s):  
Benjamin Allen ◽  
Jeff Gore ◽  
Martin A Nowak
Keyword(s):  
Public Goods ◽  
Public Good ◽  
Evolutionary Biology ◽  
Simple Relation ◽  
Evolution Of Cooperation ◽  
Previous Theory ◽  
Small Diffusion ◽  
The Public ◽  
Rates Of Decay ◽  
New Phenomena

The emergence of cooperation is a central question in evolutionary biology. Microorganisms often cooperate by producing a chemical resource (a public good) that benefits other cells. The sharing of public goods depends on their diffusion through space. Previous theory suggests that spatial structure can promote evolution of cooperation, but the diffusion of public goods introduces new phenomena that must be modeled explicitly. We develop an approach where colony geometry and public good diffusion are described by graphs. We find that the success of cooperation depends on a simple relation between the benefits and costs of the public good, the amount retained by a producer, and the average amount retained by each of the producer’s neighbors. These quantities are derived as analytic functions of the graph topology and diffusion rate. In general, cooperation is favored for small diffusion rates, low colony dimensionality, and small rates of decay of the public good.

scholarly journals Non-linear tradeoffs allow the cooperation game to evolve from Prisoner’s Dilemma to Snow Drift

2016 ◽  
Author(s):  
Lin Chao ◽  
Santiago F. Elena
Keyword(s):  
Public Goods ◽  
Group Size ◽  
Prisoner's Dilemma ◽  
Prisoner’S Dilemma ◽  
Evolution Of Cooperation ◽  
Gene Products ◽  
The Public ◽  
Snow Drift ◽  
High Level ◽  
Level Production

The existence of cooperation, or the production of public goods, is an evolutionary problem. Cooperation is not favored because the Prisoner’s Dilemma (PD) game drives cooperators to extinction. We have re-analyzed this problem by using RNA viruses to motivate a model for the evolution of cooperation. Gene products are the public goods and group size is the number of virions co-infecting the same host cell. Our results show that if the tradeoff between replication and production of gene products is linear, PD is observed. However, if the tradeoff is nonlinear, the viruses evolve into separate lineages of ultra-defectors and ultra-cooperators as group size is increased. The nonlinearity was justified by the existence of real viral ultra-defectors, known as defective interfering (DI) particles, which gain a nonlinear advantage by being smaller. The evolution of ultra-defectors and ultra-cooperators creates the Snow Drift game, which promotes high-level production of public goods.

scholarly journals Evolution of Cooperation in Public Goods Games with Stochastic Opting-Out

Games ◽  
2018 ◽  
Vol 10 (1) ◽  
pp. 1 ◽  
Author(s):  
Alexander Ginsberg ◽  
Feng Fu
Keyword(s):  
Natural Selection ◽  
Public Goods ◽  
Return On Investment ◽  
Adaptive Dynamics ◽  
Finite Size ◽  
Evolution Of Cooperation ◽  
Public Goods Game ◽  
Finite Populations ◽  
Neutral Drift ◽  
Opting Out

We study the evolution of cooperation in group interactions where players are randomly drawn from well-mixed populations of finite size to participate in a public goods game. However, due to the possibility of unforeseen circumstances, each player has a fixed probability of being unable to participate in the game, unlike previous models which assume voluntary participation. We first study how prescribed stochastic opting-out affects cooperation in finite populations, and then generalize for the limiting case of large populations. Because we use a pairwise comparison updating rule, our results apply to both genetic and behavioral evolution mechanisms. Moreover, in the model, cooperation is favored by natural selection over both neutral drift and defection if the return on investment exceeds a threshold value depending on the population size, the game size, and a player’s probability of opting-out. Our analysis further shows that, due to the stochastic nature of the opting-out in finite populations, the threshold of return on investment needed for natural selection to favor cooperation is actually greater than the one corresponding to compulsory games with the equal expected game size. We also use adaptive dynamics to study the co-evolution of cooperation and opting-out behavior. Indeed, given rare mutations minutely different from the resident population, an analysis based on adaptive dynamics suggests that over time the population will tend towards complete defection and non-participation, and subsequently cooperators abstaining from the public goods game will stand a chance to emerge by neutral drift, thereby paving the way for the rise of participating cooperators. Nevertheless, increasing the probability of non-participation decreases the rate at which the population tends towards defection when participating. Our work sheds light on understanding how stochastic opting-out emerges in the first place and on its role in the evolution of cooperation.

The Major Transitions in Evolution

1997 ◽  
Author(s):  
John Maynard Smith ◽  
Eors Szathmary
Keyword(s):  
Full Range ◽  
Evolution Of Cooperation ◽  
Major Transitions ◽  
Insect Societies ◽  
Wide Range ◽  
Major Transition ◽  
Life Itself ◽  
History Of ◽  
Emergence Of Cooperation ◽  
Multicellular Organisms

Over the history of life there have been several major changes in the way genetic information is organized and transmitted from one generation to the next. These transitions include the origin of life itself, the first eukaryotic cells, reproduction by sexual means, the appearance of multicellular plants and animals, the emergence of cooperation and of animal societies, and the unique language ability of humans. This ambitious book provides the first unified discussion of the full range of these transitions. The authors highlight the similarities between different transitions--between the union of replicating molecules to form chromosomes and of cells to form multicellular organisms, for example--and show how understanding one transition sheds light on others. They trace a common theme throughout the history of evolution: after a major transition some entities lose the ability to replicate independently, becoming able to reproduce only as part of a larger whole. The authors investigate this pattern and why selection between entities at a lower level does not disrupt selection at more complex levels. Their explanation encompasses a compelling theory of the evolution of cooperation at all levels of complexity. Engagingly written and filled with numerous illustrations, this book can be read with enjoyment by anyone with an undergraduate training in biology. It is ideal for advanced discussion groups on evolution and includes accessible discussions of a wide range of topics, from molecular biology and linguistics to insect societies.

scholarly journals Hyperbolic Center of Mass for a System of Particles in a Two-Dimensional Space with Constant Negative Curvature: An Application to the Curved 2-Body Problem

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 531
Author(s):  
Pedro Pablo Ortega Palencia ◽  
Ruben Dario Ortiz Ortiz ◽  
Ana Magnolia Marin Ramirez
Keyword(s):  
Negative Curvature ◽  
Dimensional Space ◽  
Center Of Mass ◽  
Simple Expression ◽  
Two Dimensional ◽  
Constant Negative Curvature ◽  
Euclidean Case ◽  
System Of Particles ◽  
Material Points ◽  
The One

In this article, a simple expression for the center of mass of a system of material points in a two-dimensional surface of Gaussian constant negative curvature is given. By using the basic techniques of geometry, we obtained an expression in intrinsic coordinates, and we showed how this extends the definition for the Euclidean case. The argument is constructive and serves to define the center of mass of a system of particles on the one-dimensional hyperbolic sphere LR1.

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