One-third rules with equality: Second-order evolutionary stability conditions in finite populations

Journal of Theoretical Biology

Volumn 254, Issue 3, 2008, Pages 616-620

  Bomze, Immanuel ^a   Pawlowitsch, Christina ^b  

^a UNIVERSITY OF VIENNA   (Austria)

^b HARVARD UNIVERSITY   (United States)

Author keywords

Common interest games; Fixation probabilities; Frequency dependent Moran process; Language games

Indexed keywords

EVOLUTIONARY THEORY; FITNESS; HOMINID; LANGUAGE; MUTATION; PARTNERSHIP APPROACH; POPULATION MODELING; POPULATION SIZE; PROBABILITY;

ARTICLE; DYNAMICS; EVOLUTIONARY ALGORITHM; MUTANT; POPULATION RESEARCH; POPULATION SIZE; PRIORITY JOURNAL; PROBABILITY;

ANIMALS; COMPUTATIONAL BIOLOGY; EVOLUTION; GAME THEORY; MODELS, GENETIC; POPULATION DENSITY;

EID: 51349138670     PISSN: 00225193     EISSN: 10958541     Source Type: Journal    
DOI: 10.1016/j.jtbi.2008.06.009     Document Type: Article

References (29)

1. Ania A.B. Evolutionary stability and Nash equilibrium in finite populations with an application to price competition. J. Econ. Behav. Org. 65 (2008) 472-488
2. Cressman R. Evolutionary Dynamics and Extensive Form Games (2003), MIT Press, Cambridge, MA
3. Hamilton W.D. Extraordinary sex ratios. Science 156 (1967) 477-488
4. Hofbauer J., and Sigmund K. Evolutionary Games and Population Dynamics (1998), Cambridge University Press, Cambridge, UK
5. Hofbauer J., and Sigmund K. Evolutionary game dynamics. Bull. Am. Math. Soc. 40 (2003) 479-519
6. Hofbauer J., Schuster P., and Sigmund K. A note on evolutionary stable strategies and game dynamics. J. Theor. Biol. 81 (1979) 609-612
7. Imhof L.A., and Nowak M.A. Evolutionary game dynamics in a Wright-Fisher process. J. Math. Biol. 52 (2006) 667-681
8. Kim Y.-G., and Sobel J. An evolutionary approach to pre-play communication. Econometrica 63 (1995) 1181-1193
9. Lessard S. Long-term stability from fixation probabilities in finite populations: new perspectives for ESS theory. Theor. Popul. Biol. 68 (2005) 19-27
10. Lessard S., and Ladret V. The probability of fixation of a single mutant in an exchangeable selection model. J. Math. Biol. 54 (2007) 721-744
11. Maynard Smith J. Evolution and the Theory of Games (1982), Cambridge University Press, Cambridge, UK
12. Maynard Smith J. Can a mixed strategy be stable in a finite population?. J. Theor. Biol. 130 (1988) 247-251
13. Maynard Smith J., and Price G. The logic of animal conflict. Nature 246 (1973) 15-18
14. Nowak M.A. Evolutionary Dynamics: Exploring the Equations of Life (2006), Belknap Press of Harvard University Press
15. Nowak M.A. Five rules for the evolution of cooperation. Science 314 (2006) 1560-1563
16. Nowak M.A., and Krakauer D.C. The evolution of language. Proc. Natl. Acad. Sci. USA 96 (1999) 8028-8033
17. Nowak M.A., Sasaki A., Taylor C., and Fudenberg D. Emergence of cooperation and evolutionary stability in finite populations. Nature 428 (2004) 246-650
18. Ohtsuki H., and Nowak M.A. Evolutionary stability on graphs. J. Theor. Biol. 251 (2008) 698-707
19. Ohtsuki H., Bordalo P., and Nowak M.A. The one-third law of evolutionary dynamics. J. Theor. Biol. 249 (2007) 289-295
20. Ohtsuki H., Hauert C., Lieberman E., and Nowak M.A. A simple rule for the evolution of cooperation on graphs and social networks. Nature 441 (2006) 502-505
21. Pawlowitsch C. Finite populations choose an optimal language. J. Theor. Biol. 249 (2007) 606-616
22. Pawlowitsch C. Why evolution does not always lead to an optimal signaling system. Games Econ. Behav. 63 (2008) 203-226
23. Schaffer M.E. Evolutionarily stable strategies for a finite population and a variable contest size. J. Theor. Biol. 132 (1988) 469-478
24. Taylor P.D., and Jonker L. Evolutionary stable strategies and game dynamics. Math. Biosci. 40 (1978) 145-156
25. Trapa P., and Nowak M.A. Nash equilibria for an evolutionary language game. J. Math. Biol. 41 (2000) 172-188
26. Traulsen A., Claussen J.C., and Hauert C. Coevolutionary dynamics: from finite to infinite populations. Phys. Rev. Lett. 95 (2005) 238701-238704
27. Traulsen A., Nowak M.A., and Pacheco J.M. Stochastic dynamics of invasion and fixation. Phys. Rev. E 74 (2006) 011905-011909
28. Traulsen A., Pacheco J.M., and Nowak M.A. Pairwise comparison and selection temperature in evolutionary game dynamics. J. Theor. Biol. 246 (2007) 522-529
29. Weibull J.W. Evolutionary Game Theory (1995), MIT Press, Cambridge, MA