Emergence of cooperation and evolutionary stability in finite populations

By Martin A. Nowak, A. Sasaki, Christine Taylor, Drew Fudenberg. Nature, 2004

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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.

Subfields: Genetics, Public Health, Environmental and Occupational Health, Sociology and Political Science

View Paper: https://www.semanticscholar.org/paper/ca565584823d876544c6186caba1e33c2a04e43d

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Citations in the corpus

Evolutionary dynamics on any population structure (2016, background): “1 3 A p r i l 2 0 1 7 | V O l 5 4 4 | N A T U r E | 2 2 7 lETTEr doi:10.1038/nature21723 Evolutionary dynamics on any population structure”
Evolution, situational affordances, and the HEXACO model of personality (2016, background): “Frequency-dependent selection has been posited to play an important role in explaining variability in honesty–humility, e.g., the occurrence of psychopathic versus cooperative behaviors (Mealey, 1995; Nowak et al., 2004).”
Human strategy updating in evolutionary games (2010, background): “[30] Nowak, MA, Sasaki, A, Taylor, C, Fudenberg, D (2004) Emergence of cooperation and evolutionary stability in finite populations.”
Games on graphs (2014, background): “For BD updating, the condition is R C S > T C P , which is the same as the condition for success in large well-mixed populations [108], [65], [39], and which is never satisfied for Prisoners’ Dilemma games (T > R > P > S).”
Know when to walk away: contingent movement and the evolution of cooperation. (2004, background): “Although the term ESS, as originally formulated, does not strictly apply to this model because this model is made up of a finite number of agents (Nowak et al., 2004), the resistance of Walk Away to invasion by other strategies is nonetheless investigated here.”
Models of cooperation based on the Prisoner's Dilemma and the Snowdrift game (2005, background): “By studying stochastic game dynamics in finite populations, Nowak et al. (2004) have recently argued that cooperation in the IPD may be enhanced by small population sizes.”
Fixation times in evolutionary games under weak selection (2008, background): “Moreover, it allows analytical approximations that are often impossible when selective di erences in payo s are large [8, 24, 25].”
Learning and Equilibrium (2009, methodology): “In the absence of mutations ot other perturbations, the Binmore & Samuelson (1997) and the Nowak et al. (2004) models both have the property that every “homogeneous” state where all agents play the same strategy is absorbing, while every state where two or more strategies are played is transient.”
EVOLUTIONARY DYNAMICS OF CLIMATE CHANGE UNDER COLLECTIVE-RISK DILEMMAS (2012, background): “For such population sizes, stochastic effects play an important role and the deterministic description of the previous section may be too simplistic.(52) For finite, well-mixed populations of size Z, the binomial sampling in Eqs.”