Skip to main content
Erschienen in: Dynamic Games and Applications 2/2015

01.06.2015

An Effective Replicator Equation for Games with a Continuous Strategy Set

verfasst von: M. Ruijgrok, Th. W. Ruijgrok

Erschienen in: Dynamic Games and Applications | Ausgabe 2/2015

Einloggen

Aktivieren Sie unsere intelligente Suche um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

The replicator equation for a two-person symmetric game, which has an interval of the real line as strategy space, is extended with a mutation term. Assuming that the distribution of the strategies has a continuous density, a partial differential equation for this density is derived. The equation is analysed for two examples. A connection is made with the canonical equation from adaptive dynamics and the continuous stable strategy criterion.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

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

  • über 102.000 Bücher
  • über 537 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

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

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




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

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




Jetzt Wissensvorsprung sichern!

Anhänge
Nur mit Berechtigung zugänglich
Literatur
1.
Zurück zum Zitat Arfken GB, Weber HJ (2012) Mathematical methods for physicists, 7th edn. Academic Press, Oxford Arfken GB, Weber HJ (2012) Mathematical methods for physicists, 7th edn. Academic Press, Oxford
2.
Zurück zum Zitat Bürger R, Bomze IM (1996) Stationary distributions under mutation-selection balance: structure and properties. Adv Appl Prob 28:227–251 Bürger R, Bomze IM (1996) Stationary distributions under mutation-selection balance: structure and properties. Adv Appl Prob 28:227–251
3.
Zurück zum Zitat Champagnat N, Ferrière R, Méléard S (2006) Unifying evolutionary dynamics: from individual stochastic processes to macroscopic models. Theor Popul Biol 69:297–321CrossRefMATH Champagnat N, Ferrière R, Méléard S (2006) Unifying evolutionary dynamics: from individual stochastic processes to macroscopic models. Theor Popul Biol 69:297–321CrossRefMATH
4.
Zurück zum Zitat Cressman R, Hofbauer J (2005) Measure dynamics on a one-dimensional continuous trait space: theoretical foundations for adaptive dynamics. Theor Popul Biol 67:47–59 Cressman R, Hofbauer J (2005) Measure dynamics on a one-dimensional continuous trait space: theoretical foundations for adaptive dynamics. Theor Popul Biol 67:47–59
5.
Zurück zum Zitat Cressman R, Hofbauer J, Riedel F (2006) Stability of the replicator equation for a single-species with a multi-dimensional trait space. J Theor Biol 239:273–288CrossRefMathSciNet Cressman R, Hofbauer J, Riedel F (2006) Stability of the replicator equation for a single-species with a multi-dimensional trait space. J Theor Biol 239:273–288CrossRefMathSciNet
6.
Zurück zum Zitat Dieckmann U, Law R (1996) The dynamical theory of coevolution: a derivation from stochastic ecological processes. J Math Biol 34:579–612CrossRefMATHMathSciNet Dieckmann U, Law R (1996) The dynamical theory of coevolution: a derivation from stochastic ecological processes. J Math Biol 34:579–612CrossRefMATHMathSciNet
7.
Zurück zum Zitat Diekmann O (2004) A beginner’s guide to adaptive dynamics. In: Rudnicki R (ed) Mathematical modelling of population dynamics, vol 63. Banach Center Publications, Institute of Mathematics, Polish Academy of Sciences, Poland, pp 47–86 Diekmann O (2004) A beginner’s guide to adaptive dynamics. In: Rudnicki R (ed) Mathematical modelling of population dynamics, vol 63. Banach Center Publications, Institute of Mathematics, Polish Academy of Sciences, Poland, pp 47–86
8.
Zurück zum Zitat Friedman D, Ostrov DN (2013) Evolutionary dynamics over continuous action spaces for population games that arise from symmetric two-player games. J Econ Theory 148(2):743–777CrossRefMATHMathSciNet Friedman D, Ostrov DN (2013) Evolutionary dynamics over continuous action spaces for population games that arise from symmetric two-player games. J Econ Theory 148(2):743–777CrossRefMATHMathSciNet
9.
Zurück zum Zitat van Kampen NG (2007) Stochastic processes in physics and chemistry, 3rd edn. Elsevier, Amsterdam van Kampen NG (2007) Stochastic processes in physics and chemistry, 3rd edn. Elsevier, Amsterdam
10.
Zurück zum Zitat Kimura M (1965) A stochastic model concerning the maintenance of genetic variability in quantitative characters. Proc Natl Acad Sci USA 54:731–736CrossRefMATH Kimura M (1965) A stochastic model concerning the maintenance of genetic variability in quantitative characters. Proc Natl Acad Sci USA 54:731–736CrossRefMATH
12.
Zurück zum Zitat Oechssler J, Riedel F (2002) On the dynamic foundation of evolutionary stability in continuous models. J Econ Theory 107:223–252CrossRefMATHMathSciNet Oechssler J, Riedel F (2002) On the dynamic foundation of evolutionary stability in continuous models. J Econ Theory 107:223–252CrossRefMATHMathSciNet
13.
14.
Zurück zum Zitat Pao CV (1992) Nonlinear parabolic and elliptic equations. Plenum Press, New YorkMATH Pao CV (1992) Nonlinear parabolic and elliptic equations. Plenum Press, New YorkMATH
15.
16.
Zurück zum Zitat Wei J, Norman E (1964) On the global representations of the solutions of linear differential equations as a product of exponentials. Proc Am Math Soc 15:327–334CrossRefMATHMathSciNet Wei J, Norman E (1964) On the global representations of the solutions of linear differential equations as a product of exponentials. Proc Am Math Soc 15:327–334CrossRefMATHMathSciNet
Metadaten
Titel
An Effective Replicator Equation for Games with a Continuous Strategy Set
verfasst von
M. Ruijgrok
Th. W. Ruijgrok
Publikationsdatum
01.06.2015
Verlag
Springer US
Erschienen in
Dynamic Games and Applications / Ausgabe 2/2015
Print ISSN: 2153-0785
Elektronische ISSN: 2153-0793
DOI
https://doi.org/10.1007/s13235-014-0118-y

Weitere Artikel der Ausgabe 2/2015

Dynamic Games and Applications 2/2015 Zur Ausgabe