Emergence of cooperation and evolutionary stability in finite populations

Martin A NowakDrew Fudenberg


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.


Jan 21, 1979·Journal of Theoretical Biology·J G Riley
May 1, 1975·British Journal of Obstetrics and Gynaecology·J M KjeldT R Fraser
Jun 22, 1988·Journal of Theoretical Biology·M E Schaffer
Feb 17, 1968·Nature·M Kimura
Mar 27, 1981·Science·R Axelrod, W D Hamilton
Jun 19, 1998·Journal of Theoretical Biology·T Killingback, Michael Doebeli
Apr 3, 2001·Science·Thomas PfeifferSebastian Bonhoeffer
Mar 13, 2003·Proceedings of the National Academy of Sciences of the United States of America·Robert BoydPeter J Richerson
Oct 24, 2003·Nature·Ernst Fehr, Urs Fischbacher


Feb 8, 2006·Journal of Mathematical Biology·Lorens A Imhof, Martin A Nowak
Jan 26, 2007·Journal of Mathematical Biology·Sabin Lessard, Véronique Ladret
Sep 25, 2010·Journal of Mathematical Biology·Peter A I Forsyth, Christoph Hauert
Jun 1, 2011·Journal of Mathematical Biology·Bin WuArne Traulsen
Dec 19, 2009·Animal Cognition·Christelle Scheid, Ronald Noë
Nov 7, 2006·Bulletin of Mathematical Biology·Tibor Antal, István Scheuring
Nov 16, 2006·Bulletin of Mathematical Biology·Max Shpak, Stephen R Proulx
Apr 4, 2008·Bulletin of Mathematical Biology·Arne TraulsenMartin A Nowak
Oct 12, 2012·Bulletin of Mathematical Biology·József Garay, Tamás F Móri
Mar 8, 2008·Theory in Biosciences = Theorie in Den Biowissenschaften·José F Fontanari, Leonid I Perlovsky
May 3, 2005·Journal of Theoretical Biology·Angel Sánchez, José A Cuesta
Oct 22, 2013·Journal of Theoretical Biology·Maria Abou Chakra, Arne Traulsen
Jul 3, 2013·Theoretical Population Biology·Max ShpakErnest Barany
Oct 28, 2005·Nature·Martin A Nowak, Karl Sigmund
May 26, 2006·Nature·Hisashi OhtsukiMartin A Nowak
Aug 19, 2011·Nature Communications·David G Rand, Martin A Nowak
Jun 28, 2012·Nature Communications·Weini HuangArne Traulsen
May 13, 2009·Proceedings of the National Academy of Sciences of the United States of America·Corina E TarnitaMartin A Nowak
Mar 10, 2010·Proceedings of the National Academy of Sciences of the United States of America·Chaitanya S Gokhale, Arne Traulsen
Feb 10, 2010·Proceedings of the National Academy of Sciences of the United States of America·Arne TraulsenManfred Milinski
Jun 11, 2011·Proceedings of the National Academy of Sciences of the United States of America·Francisco C Santos, Jorge M Pacheco
Jan 25, 2011·Proceedings of the National Academy of Sciences of the United States of America·Corina E TarnitaMartin A Nowak
Apr 11, 2013·Proceedings of the National Academy of Sciences of the United States of America·Christian HilbeKarl Sigmund
Sep 5, 2013·Proceedings of the National Academy of Sciences of the United States of America·Alexander J Stewart, Joshua B Plotkin
May 29, 2008·Biology Letters·Lindsay C YoungEric A Vanderwerf
Dec 14, 2004·Proceedings. Biological Sciences·Geoff Wild, Peter Taylor
Jul 19, 2005·Proceedings. Biological Sciences·Thomas PfeifferSebastian Bonhoeffer
Aug 12, 2006·Proceedings. Biological Sciences·Hisashi Ohtsuki, Martin A Nowak
Sep 25, 2008·Proceedings. Biological Sciences·Jorge M PachecoBrian Skyrms
Jan 15, 2009·Proceedings. Biological Sciences·Shun Kurokawa, Yasuo Ihara
Oct 23, 2009·Proceedings. Biological Sciences·Lorens A Imhof, Martin A Nowak
Sep 15, 2012·Proceedings. Biological Sciences·Peter Taylor, Wes Maciejewski
Dec 14, 2004·Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences·Terrence Chorvat, Kevin McCabe
Dec 17, 2009·Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences·Martin A NowakTibor Antal
Feb 16, 2011·Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences·Yasuo Ihara
Dec 13, 2006·Science·Martin A Nowak
Jun 30, 2007·Science·Christoph HauertKarl Sigmund
Jun 25, 2008·Artificial Life·Richard StaffordGray A Williams
Sep 4, 2012·Artificial Life·The Anh HanFrancisco C Santos
May 12, 2012·BMC Evolutionary Biology·Bahram Houchmandzadeh, Marcel Vallade
Mar 17, 2006·BMC Microbiology·Scot E Dowd, Hiroshi Ishizaki
Dec 17, 2009·PLoS Computational Biology·Jorge M PachecoFrancisco C Santos
Dec 19, 2009·PLoS Computational Biology·Charles G NathansonMartin A Nowak
Oct 16, 2010·PLoS Computational Biology·Dimitris IliopoulosChristoph Adami
Nov 11, 2011·PLoS Computational Biology·Philipp M AltrockFloyd A Reed
Apr 19, 2012·PLoS Computational Biology·Martial L Ndeffo MbahAlison P Galvani

Related Concepts

Trending Feeds


Coronaviruses encompass a large family of viruses that cause the common cold as well as more serious diseases, such as the ongoing outbreak of coronavirus disease 2019 (COVID-19; formally known as 2019-nCoV). Coronaviruses can spread from animals to humans; symptoms include fever, cough, shortness of breath, and breathing difficulties; in more severe cases, infection can lead to death. This feed covers recent research on COVID-19.

STING Receptor Agonists

Stimulator of IFN genes (STING) are a group of transmembrane proteins that are involved in the induction of type I interferon that is important in the innate immune response. The stimulation of STING has been an active area of research in the treatment of cancer and infectious diseases. Here is the latest research on STING receptor agonists.

Chronic Fatigue Syndrome

Chronic fatigue syndrome is a disease characterized by unexplained disabling fatigue; the pathology of which is incompletely understood. Discover the latest research on chronic fatigue syndrome here.

Hereditary Sensory Autonomic Neuropathy

Hereditary Sensory Autonomic Neuropathies are a group of inherited neurodegenerative disorders characterized clinically by loss of sensation and autonomic dysfunction. Here is the latest research on these neuropathies.

Glut1 Deficiency

Glut1 deficiency, an autosomal dominant, genetic metabolic disorder associated with a deficiency of GLUT1, the protein that transports glucose across the blood brain barrier, is characterized by mental and motor developmental delays and infantile seizures. Follow the latest research on Glut1 deficiency with this feed.

Regulation of Vocal-Motor Plasticity

Dopaminergic projections to the basal ganglia and nucleus accumbens shape the learning and plasticity of motivated behaviors across species including the regulation of vocal-motor plasticity and performance in songbirds. Discover the latest research on the regulation of vocal-motor plasticity here.

Neural Activity: Imaging

Imaging of neural activity in vivo has developed rapidly recently with the advancement of fluorescence microscopy, including new applications using miniaturized microscopes (miniscopes). This feed follows the progress in this growing field.

Nodding Syndrome

Nodding Syndrome is a neurological and epileptiform disorder characterized by psychomotor, mental, and growth retardation. Discover the latest research on Nodding Syndrome here.

LRRK2 & Microtubules

Mutations in the LRRK2 gene are risk-factors for developing Parkinson’s disease (PD). LRRK2 mutations in PD have been shown to enhance its association with microtubules. Here is the latest research.

Related Papers

Bulletin of Mathematical Biology
Christine TaylorMartin A Nowak
Journal of Mathematical Biology
Lorens A Imhof, Martin A Nowak
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Arne TraulsenJorge M Pacheco
© 2021 Meta ULC. All rights reserved