Reciprocity and repeated games have been at the center of attention when studying the evolution of human cooperation. Direct reciprocity is considered to be a powerful mechanism for the evolution of cooperation, and it is generally assumed that it can lead to high levels of cooperation. Here we explore an openended, infinite strategy space, where every strategy that can be encoded by a finite state automaton is a possible mutant. Surprisingly, we find that direct reciprocity alone does not lead to high levels of cooperation. Instead we observe perpetual oscillations between cooperation and defection, with defection being substantially more frequent than cooperation. The reason for this is that "indirect invasions" remove equilibrium strategies: every strategy has neutral mutants, which in turn can be invaded by other strategies. However, reciprocity is not the only way to promote cooperation. Another mechanism for the evolution of cooperation, which has received as much attention, is assortment because of population structure. Here we develop a theory that allows us to study the synergistic interaction between direct reciprocity and assortment. This framework is particularly well suited for understanding human interactions, which are typically repeated and occur in relatively fluid but not unstructured populations. We show that if repeated games are combined with only a small amount of assortment, then natural selection favors the behavior typically observed among humans: high levels of cooperation implemented using conditional strategies. repeated prisoner's dilemma | game theory T he problem of cooperation in its simplest and most challenging form is captured by the Prisoners' Dilemma. Two people can choose between cooperation and defection. If both cooperate, they get more than if both defect, but if one defects and the other cooperates, the defector gets the highest payoff and the cooperator gets the lowest. In the one-shot Prisoners' Dilemma, it is in each person's interest to defect, even though both would be better off had they cooperated. This game illustrates the tension between private and common interest.However, people often cooperate in social dilemmas. Explaining this apparent paradox has been a major focus of research across fields for decades. Two important explanations for the evolution of cooperation that have emerged are reciprocity (1-19) and population structure (20)(21)(22)(23)(24)(25)(26)(27)(28)(29)(30)(31)(32). If individuals find themselves in a repeated Prisoner's Dilemma-rather than a one-shot version-then there are Nash equilibria where both players cooperate under the threat of retaliation in future rounds (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19). The existence of such equilibria is a cornerstone result in economics (1-3), and the evolution of cooperation in repeated games is of shared interest for biology (4-10), economics (11)(12)(13)(14), psychology (15), and sociology (16), with applications that range from antitrust laws (17) to sticklebacks (18), alt...

Group selection, kin selection, altruism and cooperation: when inclusive fitness is right and when it can be wrong van Veelen, C.M. General rightsIt is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons). Disclaimer/Complaints regulationsIf you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: http://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible. b s t r a c tGroup selection theory has a history of controversy. After a period of being in disrepute, models of group selection have regained some ground, but not without a renewed debate over their importance as a theoretical tool. In this paper I offer a simple framework for models of the evolution of altruism and cooperation that allows us to see how and to what extent both a classification with and one without group selection terminology are insightful ways of looking at the same models. Apart from this dualistic view, this paper contains a result that states that inclusive fitness correctly predicts the direction of selection for one class of models, represented by linear public goods games. Equally important is that this result has a flip side: there is a more general, but still very realistic class of models, including models with synergies, for which it is not possible to summarize their predictions on the basis of an evaluation of inclusive fitness.

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