Revisiting matrix games: The concept of neighborhood invader strategies

Theoretical Population Biology

Volumn 69, Issue 3, 2006, Pages 235-242

  Apaloo, J ^a  

^a ST FRANCIS XAVIER UNIVERSITY   (Canada)

Author keywords

Convergence stable; ESS; Matrix(G) ESS; NIS; Replicator dynamics

Indexed keywords

EVOLUTIONARILY STABLE STRATEGY; GAME THEORY; MATRIX;

ANIMAL; ANIMAL BEHAVIOR; ARTICLE; BEHAVIOR; BIOLOGICAL MODEL; EVOLUTION; GAME; GENE FREQUENCY; HUMAN; MUTATION; POPULATION GENETICS; THEORETICAL MODEL;

ANIMALS; BEHAVIOR; BEHAVIOR, ANIMAL; BIOLOGICAL EVOLUTION; EVOLUTION; GAME THEORY; GENE FREQUENCY; GENETICS, POPULATION; HUMANS; MODELS, GENETIC; MODELS, THEORETICAL; MUTATION;

EID: 33645739363     PISSN: 00405809     EISSN: 10960325     Source Type: Journal    
DOI: 10.1016/j.tpb.2005.11.006     Document Type: Article

References (37)

1. Apaloo J. Revisiting strategic models of evolution: the concept of neighborhood invader strategies. Theor. Popul. Biol. 52 1 (1997) 71-77
2. Apaloo J. Ecological species coevolution. J. Biol. Syst. 5 1 (1997) 17-34
3. Apaloo J. Single species evolutionary dynamics. Evol. Ecol. 5 1 (2003) 33-49
4. Apaloo J. Multi-species evolutionary dynamics. Evol. Ecol. 18 4 (2005) 55-77
5. Apaloo J. Inaccessible continuously stable strategies. Nat. Resour. Modeling 19 (2005) 521-535
6. Auslander D.J., Guckenheimer J.M., and Oster G. Random evolutionary stable strategies. Theor. Popul. Biol. 13 (1978) 276-293
7. Bishop D.T., and Cannings C. A generalized war of attrition. J. Theor. Biol. 70 (1978) 85-124
8. Brown J.S., and Vincent T.L. A theory for the evolutionary game. Theor. Popul. Biol. 31 (1987) 140-166
9. Christiansen F.B. On conditions for evolutionary stability for continuously varying character. Am. Nat. 138 (1991) 37-50
10. Cressman, R., 1992. The stability concept of evolutionary game theory: a dynamic approach. Lecture Notes in Biomathematics, vol. 94. Springer, Berlin.
11. Cressman R. Stability of the replicator equation with continuous strategy space. Math. Soc. Sci. 50 (2005) 127-147
12. Cressman R., and Hofbauer J. Measure dynamics on a one-dimensional continuous trait space: theoretical foundations for adaptive dynamics. Theor. Popul. Biol. 67 (2005) 47-59
13. Cressman, R., Hofbauer, J., Riedel, F., Stability of the replicator equation for a single-species with a multi-dimensional continuous trait space. J. Theor. Biol., in press.
14. Dokumaci, E., Sandholm, W.H., 2005. Dynamo Version 1.2.1 (April 20).
15. Eshel I. Evolutionary and continuous stability. J. Theor. Biol. 103 (1983) 99-111
16. Eshel I., and Motro U. Kin selection and strong evolutionary stability of mutual help. Theor. Popul. Biol. 19 (1981) 420-433
17. Eshel I., and Sansone E. Evolutionary and dynamic stability in continuous population games. J. Math. Biol. 46 (2003) 445-459
18. Hamilton W.D., and May R.M. Dispersal in stable habitats. Nature 269 (1977) 578-581
19. Hofbauer J., and Sigmund K. The Theory of Evolution and Dynamical Systems (1988), Cambridge University Press, Cambridge
20. Hofbauer J., and Sigmund K. Evolutionary Games and Population Dynamics (1998), Cambridge University Press, Cambridge
21. Kisdi, É., Meszéna, G., 1993. Density dependent life history evolution in fluctuating environments. In: Yoshimura, J., Clark, C. (Eds.), Adaptation in a Stochastic Environment, Lecture Notes in Biomathematics, vol. 99. Springer, Berlin, pp. 26-62.
22. Kisdi E., and Meszéna G. Life histories with lottery competition in a stochastic environment: ESSs which do not prevail. Theor. Popul. Biol. 47 (1995) 191-211
23. Lessard S. Evolutionary stability: one concept, several meanings. Theor. Popul. Biol. 37 (1990) 159-170
24. Livnat A., Pacala W., and Levin S.A. The evolution of intergenerational discounting in offspring quality. Am. Nat. 165 3 (2005) 311-321
25. Ludwig D., and Levin S.A. Evolutionary stability of plant communities and the maintenance of multiple dispersal types. Theor. Popul. Biol. 40 (1991) 284-307
26. Maynard Smith J. Evolution and the Theory of Games (1982), Cambridge University Press, Cambridge
27. Maynard Smith J., and Price G.R. The logic of animal conflict. Nature 246 (1973) 15-18
28. McKelvey R., and Apaloo J. The structure and evolution of competition-organized ecological communities. Rocky Mount. J. Math. 25 1 (1995) 417-436
29. Meszéna G., Kisdi E., Dieckmann U., Geritz S.A.H., and Metz J.A.J. Evolutionary optimisation models and matrix games in the unified perspective of adaptive dynamics. Selection 2 1-2 (2001) 193-210
30. Nowak M. An evolutionary stable strategy may be inaccessible. J. Theor. Biol. 142 (1990) 237-241
31. Oechssler J., and Riedel F. On the dynamic foundation of evolutionary stability in continuous models. J. Econ. Theory 107 (2002) 223-252
32. Parker G.A. Evolutionary stable strategies. In: Krebs J.R., and Davis N.B. (Eds). Behavioral Ecology: An Evolutionary Approach (1984), Sinauer, Sunderland, Mass 30-61
33. Riechert S.E., and Hammerstein P. Game theory in the ecological context. Ann. Rev. Ecol. Syst. 14 (1983) 377-409
34. Taylor P.D. Evolutionary stability in one parameter models under weak selection. Theor. Popul. Biol. 36 (1989) 125-143
35. Vincent T.L., and Cressman R. An ESS maximum principle for matrix games. Theor. Popul. Biol. 58 (2000) 173-186
36. Vincent T.L., Van M.V., and Goh B.S. Ecological stability, evolutionary stability and the ESS maximum principle. Evol. Ecol. 10 (1996) 567-591
37. Wild G., and Taylor P.D. Fitness and evolutionary stability in game theoretic models of finite populations. Proc. R. Soc. London B 271 (2004) 2345-2349