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      Evolutionary dynamics with game transitions

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          Evolving populations are constantly subjected to changing environmental conditions. The environment can determine how the expression of traits affects the individuals possessing them. Just as important, however, is the fact that the expression of traits can also alter the environment. We model this phenomenon by introducing game transitions into classical models of evolutionary dynamics. Interacting individuals receive payoffs from the games that they play, and these games can change based on past actions. We find that game transitions can significantly reduce the critical benefit-to-cost threshold for cooperation to evolve in social dilemmas. This result improves our understanding of when cooperators can thrive in nature, even when classical results predict a high critical threshold.

          Abstract

          The environment has a strong influence on a population’s evolutionary dynamics. Driven by both intrinsic and external factors, the environment is subject to continual change in nature. To capture an ever-changing environment, we consider a model of evolutionary dynamics with game transitions, where individuals’ behaviors together with the games that they play in one time step influence the games to be played in the next time step. Within this model, we study the evolution of cooperation in structured populations and find a simple rule: Weak selection favors cooperation over defection if the ratio of the benefit provided by an altruistic behavior, b , to the corresponding cost, c , exceeds k k , where k is the average number of neighbors of an individual and k captures the effects of the game transitions. Even if cooperation cannot be favored in each individual game, allowing for a transition to a relatively valuable game after mutual cooperation and to a less valuable game after defection can result in a favorable outcome for cooperation. In particular, small variations in different games being played can promote cooperation markedly. Our results suggest that simple game transitions can serve as a mechanism for supporting prosocial behaviors in highly connected populations.

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          Most cited references33

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          Evolutionary games and spatial chaos

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            A simple rule for the evolution of cooperation on graphs and social networks.

            A fundamental aspect of all biological systems is cooperation. Cooperative interactions are required for many levels of biological organization ranging from single cells to groups of animals. Human society is based to a large extent on mechanisms that promote cooperation. It is well known that in unstructured populations, natural selection favours defectors over cooperators. There is much current interest, however, in studying evolutionary games in structured populations and on graphs. These efforts recognize the fact that who-meets-whom is not random, but determined by spatial relationships or social networks. Here we describe a surprisingly simple rule that is a good approximation for all graphs that we have analysed, including cycles, spatial lattices, random regular graphs, random graphs and scale-free networks: natural selection favours cooperation, if the benefit of the altruistic act, b, divided by the cost, c, exceeds the average number of neighbours, k, which means b/c > k. In this case, cooperation can evolve as a consequence of 'social viscosity' even in the absence of reputation effects or strategic complexity.
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              Emergence of cooperation and evolutionary stability in finite populations.

              To explain the evolution of cooperation by natural selection has been a major goal of biologists since Darwin. Cooperators help others at a cost to themselves, while defectors receive the benefits of altruism without providing any help in return. The standard game dynamical formulation is the 'Prisoner's Dilemma', in which two players have a choice between cooperation and defection. In the repeated game, cooperators using direct reciprocity cannot be exploited by defectors, but it is unclear how such cooperators can arise in the first place. In general, defectors are stable against invasion by cooperators. This understanding is based on traditional concepts of evolutionary stability and dynamics in infinite populations. Here we study evolutionary game dynamics in finite populations. We show that a single cooperator using a strategy like 'tit-for-tat' can invade a population of defectors with a probability that corresponds to a net selective advantage. We specify the conditions required for natural selection to favour the emergence of cooperation and define evolutionary stability in finite populations.
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                Author and article information

                Journal
                Proc Natl Acad Sci U S A
                Proc. Natl. Acad. Sci. U.S.A
                pnas
                pnas
                PNAS
                Proceedings of the National Academy of Sciences of the United States of America
                National Academy of Sciences
                0027-8424
                1091-6490
                17 December 2019
                26 November 2019
                26 November 2019
                : 116
                : 51
                : 25398-25404
                Affiliations
                [1] aCenter for Systems and Control, College of Engineering, Peking University , Beijing 100871, China;
                [2] bProgram for Evolutionary Dynamics, Harvard University , Cambridge, MA 02138;
                [3] cDepartment of Organismic and Evolutionary Biology, Harvard University , Cambridge, MA 02138;
                [4] dDepartment of Mathematics, Harvard University , Cambridge, MA 02138
                Author notes

                Edited by Nils Chr. Stenseth, University of Oslo, Oslo, Norway, and approved October 30, 2019 (received for review May 24, 2019)

                Author contributions: Q.S., A.M., L.W., and M.A.N. designed research; Q.S. and A.M. performed research; Q.S. and A.M. contributed new reagents/analytic tools; Q.S., A.M., L.W., and M.A.N. analyzed data; Q.S. wrote the supporting information; and Q.S. and A.M. wrote the paper.

                Author information
                http://orcid.org/0000-0002-9110-4635
                http://orcid.org/0000-0001-5489-0908
                Article
                201908936
                10.1073/pnas.1908936116
                6926053
                31772008
                d5244c31-af61-44e7-a71c-793cc0c24dfe
                Copyright © 2019 the Author(s). Published by PNAS.

                This open access article is distributed under Creative Commons Attribution License 4.0 (CC BY).

                History
                Page count
                Pages: 7
                Categories
                PNAS Plus
                Physical Sciences
                Applied Mathematics
                Biological Sciences
                Evolution
                PNAS Plus

                cooperation,evolutionary game theory,game transitions,structured populations

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