Abstract
This paper deals with a mathematical game. As the name implies, the game concept is formulated with biological evolution in mind. An evolutionary game differs from the usual game concepts in that the players cannot choose their strategies. Rather, the strategies used by the players are handed down from generation to generation. It is the survival characteristics of a strategy that determine the outcome of the evolutionary game. Players interact and receive payoffs according to the strategies they are using. These interactions, in turn, determine the fitness of players using a given strategy. The survival characteristics of strategy are determined directly from the fitness functions. Necessary conditions for determining an evolutionarily stable strategy are developed here for a continuous game. Results are illustrated with an example.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Von Neumann, J., andMorgenstern, O.,Theory of Games and Economic Behavior, Princeton University Press, Princeton, New Jersey, 1944.
Vincent, T. L., andGrantham, W. J.,Optimality in Parametric Systems, Wiley-Interscience, New York, New York, 1981.
Isaacs, R.,Differential Games, John Wiley and Sons, New York, New York, 1965.
Blaquiere, A., Gerard, F., andLeitmann, G.,Quantitative and Qualitative Games, Academic Press, New York, New York, 1969.
Leitmann, G.,Cooperative and Noncooperative Many-Players Differential Games, Springer Verlag, Vienna, Austria, 1974.
Pareto, V.,Cours d'Economie Politique, Rouge, Lausanne, Switzerland, 1896.
Nash, J. F.,Noncooperative Games, Annals of Mathematics, Vol. 54, No. 2, 1951.
Von Stackelberg, H.,The Theory of the Market Economy, Oxford University Press, Oxford, England, 1952.
Leitmann, G.,Collective Bargaining: A Differential Game, Journal of Optimization Theory and Applications, Vol. 11, pp. 405–412, 1973.
Chen, S. F., andLeitmann, G.,Labor-Management Bargaining Modelled as a Dynamic Game, Optimal Control Applications and Methods, Vol. 1, pp. 11–25, 1980.
Leitmann, G., andSkowronski, J.,Avoidance Control, Journal of Optimization Theory and Applications, Vol. 23, pp. 581–591, 1977.
Peng, W. Y., andVincent, T. L.,Some Aspects of Aerial Combat, AIAA Journal, Vol. 13, pp. 7–11, 1975.
Simaan, M., andCruz, J. B., Jr.,A Multistage Game Formulation of Arms Race and Control and Its Relationship to Richardson's Model, Modeling and Simulation, Vol. 4, Edited by W. G. Vogt and M. H. Mickle, Instrument Society of America, Pittsburgh, Pennsylvania, pp. 149–153, 1973.
Auslander, D. J., Guckenheimer, J. M., andOster, G.,Random Evolutionary Stable Strategies, Theoretical Population Biology, Vol. 13, pp. 276–293, 1978.
Mirmirani, M., andOster, G.,Competition, Kin Selection, and Evolutionary Stable Strategies, Theoretical Population Biology, Vol. 13, pp. 304–339, 1978.
Vincent, T. L.,Environmental Adaptation by Annual Plants (An Optimal Controls/Games Viewpoint), Differential Games and Applications: Proceedings of a Workshop (Lecture Notes in Control and Information Sciences, Vol. 3), Edited by P. Hagedorn, Springer-Verlag, Berlin, Germany, 1977.
Maynard Smith, J.,Evolution and the Theory of Games, Cambridge University Press, Cambridge, England, 1982.
Vincent, T. L., andBrown, J. S.,Stability in an Evolutionary Game, Theoretical Population Biology, Vol. 26, pp. 408–427, 1984.
Dawkins, R.,The Selfish Gene, Oxford University Press, New York, New York, 1976.
Author information
Authors and Affiliations
Additional information
Dedicated to G. Leitmann
This work was supported by NSF Grant No. INT-82-10803 and The University of Western Australia (Visiting Fellowship, Department of Mathematics, 1983).
Rights and permissions
About this article
Cite this article
Vincent, T.L. Evolutionary games. J Optim Theory Appl 46, 605–612 (1985). https://doi.org/10.1007/BF00939163
Issue Date:
DOI: https://doi.org/10.1007/BF00939163