Skip to main content
main-content

Tipp

Weitere Artikel dieser Ausgabe durch Wischen aufrufen

Erschienen in: Dynamic Games and Applications 4/2021

17.04.2021

Effect of Variability in Payoffs on Conditions for the Evolution of Cooperation in a Small Population

verfasst von: Dhaker Kroumi, Éloi Martin, Cong Li, Sabin Lessard

Erschienen in: Dynamic Games and Applications | Ausgabe 4/2021

Einloggen, um Zugang zu erhalten
share
TEILEN

Abstract

In this paper, we study the effect of stochastic fluctuations in payoffs for two strategies, cooperation and defection, used in random pairwise interactions in a population of fixed finite size with an update according to a Moran model. We assume that the means, variances and covariances of the payoffs are of the same small order while all higher-order moments are negligible. We show that more variability in the payoffs to defection and less variability in the payoffs to cooperation contribute to the evolutionary success of cooperation over defection as measured by fixation probabilities under weak selection. This conclusion is drawn by comparing the probabilities of ultimate fixation of cooperation and defection as single mutants to each other and to what they would be under neutrality. These comparisons are examined in detail with respect to the population size and the second moments of the payoffs in five cases of additive Prisoner’s Dilemmas. The analysis is extended to a Prisoner’s Dilemma repeated a random number of times with Tit-for-Tat starting with cooperation and Always-Defect as strategies. Moreover, simulations with an update according to a Wright–Fisher model suggest that the conclusions are robust.

Sie möchten Zugang zu diesem Inhalt erhalten? Dann informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 69.000 Bücher
  • über 500 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Testen Sie jetzt 15 Tage kostenlos.

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 50.000 Bücher
  • über 380 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




Testen Sie jetzt 15 Tage kostenlos.

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 58.000 Bücher
  • über 300 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Testen Sie jetzt 15 Tage kostenlos.

Anhänge
Nur mit Berechtigung zugänglich
Literatur
1.
Zurück zum Zitat Antal T, Nowak MA, Traulsen A (2009) Strategy abundance in \(2\times 2\) games for arbitrary mutation rates. J Theor Biol 257:340–344 CrossRef Antal T, Nowak MA, Traulsen A (2009) Strategy abundance in \(2\times 2\) games for arbitrary mutation rates. J Theor Biol 257:340–344 CrossRef
2.
Zurück zum Zitat Broom M (2005) Evolutionary games with variable payoffs. C R Biol 328:403–412 CrossRef Broom M (2005) Evolutionary games with variable payoffs. C R Biol 328:403–412 CrossRef
3.
Zurück zum Zitat Ewens WJ (2004) Mathematical population genetics: I theoretical introduction. Springer, New York CrossRef Ewens WJ (2004) Mathematical population genetics: I theoretical introduction. Springer, New York CrossRef
5.
Zurück zum Zitat Fudenberg D, Nowak MA, Taylor C, Imhof LA (2006) Evolutionary game dynamics in finite populations with strong selection and weak mutation. Theor Popul Biol 70:352–363 CrossRef Fudenberg D, Nowak MA, Taylor C, Imhof LA (2006) Evolutionary game dynamics in finite populations with strong selection and weak mutation. Theor Popul Biol 70:352–363 CrossRef
6.
Zurück zum Zitat Hofbauer J, Sigmund K (1998) The theory of evolution and dynamical systems. Cambridge University Press, Cambridge MATH Hofbauer J, Sigmund K (1998) The theory of evolution and dynamical systems. Cambridge University Press, Cambridge MATH
7.
Zurück zum Zitat Kaplan H, Hill K, Hurtado AM (1990) Risk, foraging and food sharing among the Ache. In: Cashdan E (ed) Risk and uncertainty in tribal and peasant economies. Westview Press, Boulder, pp 107–144 Kaplan H, Hill K, Hurtado AM (1990) Risk, foraging and food sharing among the Ache. In: Cashdan E (ed) Risk and uncertainty in tribal and peasant economies. Westview Press, Boulder, pp 107–144
8.
Zurück zum Zitat Karlin S, Levikson B (1974) Temporal fluctuations in selection intensities: case of small population size. Theor Popul Biol 6:383–412 MathSciNetCrossRef Karlin S, Levikson B (1974) Temporal fluctuations in selection intensities: case of small population size. Theor Popul Biol 6:383–412 MathSciNetCrossRef
9.
Zurück zum Zitat Karlin S, Taylor P (1975) A first course in stochastic processes, 2nd edn. Academic Press, New York MATH Karlin S, Taylor P (1975) A first course in stochastic processes, 2nd edn. Academic Press, New York MATH
10.
Zurück zum Zitat Kroumi D, Lessard S (2021) The effect of variability in payoffs on average abundance in two-player linear games under symmetric mutation. J Theor Biol 513:110569 Kroumi D, Lessard S (2021) The effect of variability in payoffs on average abundance in two-player linear games under symmetric mutation. J Theor Biol 513:110569
11.
Zurück zum Zitat Lande R, Engen S, Saether B-E (2003) Stochastic population dynamics in ecology and conservation. Oxford University Press, Oxford CrossRef Lande R, Engen S, Saether B-E (2003) Stochastic population dynamics in ecology and conservation. Oxford University Press, Oxford CrossRef
12.
Zurück zum Zitat Lambert A (2006) Probability of fixation under weak selection: a branching process unifying approach. Theor Popul Biol 69:419–441 CrossRef Lambert A (2006) Probability of fixation under weak selection: a branching process unifying approach. Theor Popul Biol 69:419–441 CrossRef
13.
Zurück zum Zitat Lessard S (2005) Long-term stability from fixation probabilities in finite populations: new perspectives for ESS theory. Theor Popul Biol 68:19–27 CrossRef Lessard S (2005) Long-term stability from fixation probabilities in finite populations: new perspectives for ESS theory. Theor Popul Biol 68:19–27 CrossRef
14.
Zurück zum Zitat Lessard S (2011) Evolution of cooperation in finite populations. In: Sigmund K (ed) Evolutionary game dynamics. American Mathematical Society, Providence, pp 143–171 CrossRef Lessard S (2011) Evolution of cooperation in finite populations. In: Sigmund K (ed) Evolutionary game dynamics. American Mathematical Society, Providence, pp 143–171 CrossRef
15.
Zurück zum Zitat Li C, Lessard L (2020) Randomized matrix games in a finite population: effect of stochastic fluctuations in payoffs on the evolution of cooperation. Theor Popul Biol 143:77–91 CrossRef Li C, Lessard L (2020) Randomized matrix games in a finite population: effect of stochastic fluctuations in payoffs on the evolution of cooperation. Theor Popul Biol 143:77–91 CrossRef
16.
Zurück zum Zitat Li C, Ji T, He QQ, Zheng ZD, Zhang BY, Lessard S, Tao Y (2019) Uncertainty in payoffs for defection could be conductive to the evolution of cooperative behavior ( preprint) Li C, Ji T, He QQ, Zheng ZD, Zhang BY, Lessard S, Tao Y (2019) Uncertainty in payoffs for defection could be conductive to the evolution of cooperative behavior ( preprint)
17.
Zurück zum Zitat May RM (1973) Stability and complexity in model ecosystems. Princeton University Press, Princeton May RM (1973) Stability and complexity in model ecosystems. Princeton University Press, Princeton
18.
Zurück zum Zitat Nowak MA (2006) Evolutionary dynamics. Harvard University Press, Cambridge CrossRef Nowak MA (2006) Evolutionary dynamics. Harvard University Press, Cambridge CrossRef
19.
Zurück zum Zitat Nowak MA, Sasaki A, Taylor C, Fudenberg D (2004) Emergence of cooperation and evolutionary stability in finite populations. Nature 428:646–650 CrossRef Nowak MA, Sasaki A, Taylor C, Fudenberg D (2004) Emergence of cooperation and evolutionary stability in finite populations. Nature 428:646–650 CrossRef
20.
Zurück zum Zitat Otto SP, Whitlock MC (1997) The probability of fixation in populations of changing size. Genetics 146:723–733 CrossRef Otto SP, Whitlock MC (1997) The probability of fixation in populations of changing size. Genetics 146:723–733 CrossRef
21.
Zurück zum Zitat Parsons TL, Quince C (2007) Fixation in haploid populations exhibiting density dependence I: the non-neutral case. Theor Popul Biol 72:121–135 Parsons TL, Quince C (2007) Fixation in haploid populations exhibiting density dependence I: the non-neutral case. Theor Popul Biol 72:121–135
22.
Zurück zum Zitat Parsons TL, Quince C (2007) Fixation in haploid populations exhibiting density dependence II: the quasi-neutral case. Theor Popul Biol 72:468–479 CrossRef Parsons TL, Quince C (2007) Fixation in haploid populations exhibiting density dependence II: the quasi-neutral case. Theor Popul Biol 72:468–479 CrossRef
23.
Zurück zum Zitat Rousset F, Billiard D (2000) A theoretical basis for measures of kin selection in subdivided populations: finite populations and localized dispersal. J Evol Biol 13:814–825 CrossRef Rousset F, Billiard D (2000) A theoretical basis for measures of kin selection in subdivided populations: finite populations and localized dispersal. J Evol Biol 13:814–825 CrossRef
24.
Zurück zum Zitat Rousset F (2003) A minimal derivation of convergence stability measures. J Theor Biol 221:665–668 CrossRef Rousset F (2003) A minimal derivation of convergence stability measures. J Theor Biol 221:665–668 CrossRef
25.
Zurück zum Zitat Stollmeier F, Nagler J (2018) Unfair and anomalous evolutionary dynamics from fluctuating payoffs. Phys. Rev Lett 120:058101 Stollmeier F, Nagler J (2018) Unfair and anomalous evolutionary dynamics from fluctuating payoffs. Phys. Rev Lett 120:058101
26.
Zurück zum Zitat Tarnita C, Ohtsuki H, Antal T, Fu F, Nowak MA (2009) Strategy selection in structured populations. J Theor Biol 259:570–581 MathSciNetCrossRef Tarnita C, Ohtsuki H, Antal T, Fu F, Nowak MA (2009) Strategy selection in structured populations. J Theor Biol 259:570–581 MathSciNetCrossRef
27.
28.
Zurück zum Zitat Uecker H, Hermisson J (2011) On the fixation process of a beneficial mutation in a variable environment. Genetics 188:915–930 CrossRef Uecker H, Hermisson J (2011) On the fixation process of a beneficial mutation in a variable environment. Genetics 188:915–930 CrossRef
29.
Zurück zum Zitat Wu B, Altrock PM, Wang L, Traulsen A (2010) Universality of weak selection. Phys Rev E 82:046106 CrossRef Wu B, Altrock PM, Wang L, Traulsen A (2010) Universality of weak selection. Phys Rev E 82:046106 CrossRef
30.
Zurück zum Zitat Wu B, Traulsen A, Gokhale CS (2013) Dynamic Properties of evolutionary multi-player games in finite populations. Games 4:182–199 MathSciNetCrossRef Wu B, Traulsen A, Gokhale CS (2013) Dynamic Properties of evolutionary multi-player games in finite populations. Games 4:182–199 MathSciNetCrossRef
31.
Zurück zum Zitat Zeeman RC (1980) Populations dynamics from game theory. In: Nitecki ZH, Robinson RC (eds) Global theory of dynamical systems. Springer, New York Zeeman RC (1980) Populations dynamics from game theory. In: Nitecki ZH, Robinson RC (eds) Global theory of dynamical systems. Springer, New York
32.
Zurück zum Zitat Zheng XD, Li C, Lessard S, Tao Y (2017) Evolutionary stability concepts in a stochastic environment. Phys Rev E 96:032414 CrossRef Zheng XD, Li C, Lessard S, Tao Y (2017) Evolutionary stability concepts in a stochastic environment. Phys Rev E 96:032414 CrossRef
33.
Zurück zum Zitat Zheng XD, Li C, Lessard S, Tao Y (2018) Environmental noise could promote stochastic local stability of behavioral diversity evolution. Phys Rev Lett 120:218101 CrossRef Zheng XD, Li C, Lessard S, Tao Y (2018) Environmental noise could promote stochastic local stability of behavioral diversity evolution. Phys Rev Lett 120:218101 CrossRef
Metadaten
Titel
Effect of Variability in Payoffs on Conditions for the Evolution of Cooperation in a Small Population
verfasst von
Dhaker Kroumi
Éloi Martin
Cong Li
Sabin Lessard
Publikationsdatum
17.04.2021
Verlag
Springer US
Erschienen in
Dynamic Games and Applications / Ausgabe 4/2021
Print ISSN: 2153-0785
Elektronische ISSN: 2153-0793
DOI
https://doi.org/10.1007/s13235-021-00383-2

Weitere Artikel der Ausgabe 4/2021

Dynamic Games and Applications 4/2021 Zur Ausgabe

Premium Partner