Abstract
This article compares evolutionary equilibrium notions with solution concepts in rational game theory. Both static and dynamic evolutionary game theory are treated. The methods employed by dynamic theory, so-called “game dynamics”, could be discovered to be relevant for rational game theory also.
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References
Abakuks A (1980) Conditions for evolutionary stable strategies. J Appl Prob 17:559–562
Aigner M (1979) Combinatorial theory. Springer, Berlin Heidelberg New York (Grundl d math Wiss i Einzeld Bd 234)
Akin E (1980) Domination or equilibrium. Math Biosci 50:239–250
Akin E, Hofbauer J (1982) Recurrence of the unfit. Math Biosci 61:51–63
Auslander D, Guckenheimer J, Oster G (1978) Random evolutionarily stable strategies. Theor Pop Biol 13:276–293
Axelrod R (1981) The emergence of cooperation among egoists. Am political Sci Rev 75:306–318
Bishop DT, Cannings C (1976) Models of animal conflicts. Adv Appl Prob 6:616–621
Bishop DT, Cannings D (1978) A generalized war of attrition. J theor Biol 70:85–124
Bomze IM (1983) Lotka-Volterra equation and replicator dynamics: a two-dimensional classification. Biol Cybern 48:201–211
Bomze IM, Schuster P, Sigmund K (1983) The role of Mendelian genetics in strategic models on animal conflicts. J theor Biol 101:19–38
Brown JS, Sanderson MJ, Michod RE (1982) Evolution of social behaviour by reciprocation. J theor Biol 99:319–339
Van Damme EEC (1983) Refinements of the Nash equilibrium concept. Springer, Berlin Heidelberg New York (Lecture Notes in Economics and Mathematical Systems, vol 219)
Fisher RA (1930) The genetical theory of natural selection. Clarendon Press, Oxford
Hamilton WD (1967) Extraordinary sex ratios. Science, Wash. 156:477–488
Harsanyi JC (1973a) Games with randomly disturbed payoffs: a new rationale for mixed strategy equilibrium points. Int J Game Theory 2:1–23
Harsanyi JC (1973b) Oddness of the number of equilibrium points: a new proof. Int J Game Theory 2:235–250
Hines WGS (1980) An evolutionarily stable strategy model for randomly mating diploid populations. J theor Biol 87:379–384
Hines WGS (1982) Strategy stability in complex randomly mating diploid populations. J Appl Prob 19:653–659
Hofbauer J (1981) On the occurrence of limit cycles in the Volterra-Lotka differential equation. J Nonlinear Anal 5:1003–1007
Hofbauer J (1984) A difference equation model for the hypercycle. Siam J Appl Math 44:762–772
Hofbauer J, Sigmund K (1984) Evolutionstheorie und dynamische Systeme. Mathematische Aspekte der Selektion. Paul Parey, Berlin Hamburg
Hofbauer J, Schuster P, Sigmund K (1979) A note on evolutionary stable strategies and game dynamics. J theor Biol 81:609–612
Hofbauer J, Schuster P, Sigmund K (1982) Game dynamics in Mendelian populations. Biol Cybern 43:51–57
Hofbauer J, Schuster P, Sigmund K, Wolff R (1980) Dynamical systems under constant organisation II: Homogeneous growth functions of degreep=2. Siam J Appl Math C38:282–304
Losert V, Akin E (1983) Dynamics of games and genes: discrete versus continuous time. J Math Biol 17:241–251
Maynard Smith J (1981) Will a sexual population evolve to anESS? Am Nat 117:1015–1018
Maynard Smith J (1982) Evolution and the theory of games. Cambridge University Press, Cambridge
Maynard Smith J, Price GR (1973) The logic of animal conflict. Nature, Lond 246:15–18
Myerson RB (1978) Refinements of the Nash equilibrium concept. Int J Game Theory 7:73–80
Nash JF (1951) Non-cooperative games. Ann of Math 54:286–295
Norman MF (1981) Sociobiological variations on a Mendelian theme. In: Grossberg S (ed) Mathematical Psychology and Psychophysiology. SIAM-AMS Proceedings, vol 13:187–196
Okada A (1981) On stability of perfect equilibrium points. Int J Game Theory 10:67–73
Parthasarathy T, Raghavan TES (1971) Some topics in two-person games. In: Bellman R (ed) Modern analytic and computational methods in science and mathematics, vol 22. American Elsevier, New York
Riechert SE, Hammerstein P (1983) Game theory in the ecological context. Ann Rev Ecol Syst 14:377–409
Rothstein SI (1980) Reciprocal altruism and kin selection are not clearly separable phenomena. J theor Biol 87:255–261
Schuster P, Sigmund K (1981) Coyness, philandering and stable strategies. Anim Behav 29:186–192
Schuster P, Sigmund K (1983) Replicator dynamics. J theor Biol 100:533–538
Schuster P, Sigmund K, Wolff R (1978) Dynamical systems under constant organization I: Topological analysis of a family of non-linear differential equations. Bull Math Biophys 40:743–769
Schuster P, Sigmund K, Hofbauer J, Wolff R (1981a) Selfregulation of behaviour in animal societies I: Symmetric contests. Biol Cybern 40:1–8
Schuster P, Sigmund K, Hofbauer J, Wolff R (1981b) Selfregulation of behaviour in animal societies II: Games between two populations without selfinteraction. Biol Cybern 40:9–15
Schuster P, Sigmund K, Hofbauer J, Wolff R, Gottlieb R, Merz P (1981c) Selfregulation of behaviour in animal societies III: Games between two populations with selfinteraction. Biol Cybern 40:17–25
Taylor PD (1979) Evolutionarily stable strategies with two types of player. J Appl Prob 16:76–83
Treisman M (1977) The evolutionary restriction of aggression within a species: a game theory analysis. J Math Psychol 16:167–203
Trivers RL (1971) The evolution of reciprocal altruism. Q Rev Biol 46:35–57
Wu Wen-Tsün, Jiang Jia-He (1962) Essential equilibrium points ofn-person non-cooperative games. Sci Sinica 11:1370–1372
Zeeman EC (1980) Population dynamics from game theory. In: Global theory of dynamical systems. Nitecki Z, Robinson C (eds) Springer, Berlin Heidelberg New York (Lecture Notes in Mathematics vol 819)
Zeeman EC (1981) Dynamics of the evolution of animal conflicts. J theor Biol 89:249–270
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Bomze, I.M. Non-cooperative two-person games in biology: A classification. Int J Game Theory 15, 31–57 (1986). https://doi.org/10.1007/BF01769275
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DOI: https://doi.org/10.1007/BF01769275