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      Evolutionary dynamics of complex multiple games

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          Abstract

          Evolutionary game theory has been successful in describing phenomena from bacterial population dynamics to the evolution of social behaviour. However, it has typically focused on a single game describing the interactions between individuals. Organisms are simultaneously involved in many intraspecies and interspecies interactions. Therefore, there is a need to move from single games to multiple games. However, these interactions in nature involve many players. Shifting from 2-player games to multiple multiplayer games yield richer dynamics closer to natural settings. Such a complete picture of multiple game dynamics (MGD), where multiple players are involved, was lacking. For multiple multiplayer games—where each game could have an arbitrary finite number of players and strategies, we provide a replicator equation for MGD having many players and strategies. We show that if the individual games involved have more than two strategies, then the combined dynamics cannot be understood by looking only at individual games. Expected dynamics from single games is no longer valid, and trajectories can possess different limiting behaviour. In the case of finite populations, we formulate and calculate an essential and useful stochastic property, fixation probability. Our results highlight that studying a set of interactions defined by a single game can be misleading if we do not take the broader setting of the interactions into account. Through our results and analysis, we thus discuss and advocate the development of evolutionary game(s) theory, which will help us disentangle the complexity of multiple interactions.

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          Evolutionary games and spatial chaos

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            Collective Action and the Evolution of Social Norms

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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 Biol Sci
                Proc. Biol. Sci
                RSPB
                royprsb
                Proceedings of the Royal Society B: Biological Sciences
                The Royal Society
                0962-8452
                1471-2954
                26 June 2019
                26 June 2019
                26 June 2019
                : 286
                : 1905
                : 20190900
                Affiliations
                Research Group for Theoretical Models of Eco-evolutionary Dynamics, Department of Evolutionary Theory, Max Planck Institute for Evolutionary Biology , August Thienemann Strasse 2, 24306 Plön, Germany
                Author notes

                Electronic supplementary material is available online at http://dx.doi.org/10.6084/m9.figshare.c.4536677.

                Author information
                http://orcid.org/0000-0002-5633-9594
                http://orcid.org/0000-0002-5749-3665
                Article
                rspb20190900
                10.1098/rspb.2019.0900
                6599991
                31238846
                5d024c51-f70d-4c2d-a8d8-0c6f27d8b4be
                © 2019 The Authors.

                Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited.

                History
                : 18 April 2019
                : 31 May 2019
                Funding
                Funded by: Max-Planck-Gesellschaft, http://dx.doi.org/10.13039/501100004189;
                Categories
                1001
                203
                Evolution
                Research Article
                Custom metadata
                June 26, 2019

                Life sciences
                evolutionary game theory,multiplayer games,multiple games,finite population
                Life sciences
                evolutionary game theory, multiplayer games, multiple games, finite population

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