Abstract
A group of individuals resolve their disputes by a knockout tournament. In each round of the tournament, the remaining contestants form pairs which compete, the winners progressing to the next round and the losers being eliminated. The payoff received depends upon how far the player has progressed and a cost is incurred only when it is defeated. We only consider strategies in which individuals are constrained to adopt a fixed play throughout the successive rounds. The case where individuals can vary their choice of behaviour from round to round will be treated elsewhere. The complexity of the system is investigated and illustrated both by special cases and numerical examples.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Axelrod, R. and W. D. Hamilton (1981). The evolution of cooperation. Science 211, 1390–1396.
Barnard, C. J. and T. E. Burk (1979). Dominance hierarchies and the evolution of individual recognition. J. Theor. Biol. 81, 65–73.
Binmore, K. (1992). Fun and Games (a Text on Game Theory), Lexington, Massachusetts: Heath.
Bishop, D. T. and C. Cannings (1976). Models of animal conflict. Adv. Appl. Probab. 8, 616–621.
Broom, M., C. Cannings and G. T. Vickers (1997b). Choosing a nest site: contests and catalysts. Am. Nat. 147, 1108–1114.
Broom, M., C. Cannings and G. T. Vickers (1997a). A sequential-arrivals model of territory acquisition. J. Theor. Biol. 189, 257–272.
Broom, M., C. Cannings and G. T. Vickers (1997b). Multi-player matrix games. Bull. Math. Biol. 59, 931–952.
Cannings, C. and J. C. Whittaker (1994). The finite horizon war of attrition. Games Econ. Behav. 11, 193–236.
Cressman, R. (1992). The Stability Concept of Evolutionary Game Theory: A Dynamic Approach, Lecture Notes Biomathematics, 94, Berlin: Springer-Verlag.
Emlen, S. T. (1996). Reproductive sharing in different types of kin associations. Am. Nat. 150, 542–558.
Grafen, A. (1990a). Sexual selection unhandicapped by the Fisher process. J. Theor. Biol. 144, 473–516.
Grafen, A. (1990b). Biological signals as handicaps. J. Theor. Biol. 144, 517–546.
Haigh, J. (1975). Game theory and evolution. Adv. Appl. Probab. 7, 8–11.
Haigh, J. and C. Cannings (1989). The n-person war of attrition. Acta Appl. Math. 14, 59–74.
Hofbauer, J. and K. Sigmund (1988). The Theory of Evolution and Dynamical Systems, Lexington, Massachusetts: Cambridge University Press.
Hoglund, J. and R. V. Alatalo (1995). Leks, Princeton, NJ: Princeton University Press.
Keller, L. and H. K. Reeve (1994). Partitioning of reproduction in animal societies. Trends Ecol. Evol. 9, 98–103.
Luce, R. D. and H. Raiffa (1957). Games and Decisions, Wiley.
Maynard Smith, J. (1982). Evolution and the Theory of Games, Lexington, Massachusetts: Cambridge University Press.
Maynard Smith, J. and G. R. Price (1973). The logic of animal conflict. Nature 246, 15–18.
Mesterton-Gibbons, M. and L. A. Dugatkin (1995). Towards a theory of dominance hierarchies: effect of assessment, group size and variation in fighting ability. Behav. Ecol. 6, 416–423.
Moehlman, P. D. (1979). Jackal helpers and pup survival. Nature 277, 382–383
Reeve, H. K. and L. Keller (1996). Relatedness asymmetry and reproductive sharing in animal societies. Am. Nat. 148, 764–769.
Riley, J. G. (1979). Evolutionary equilibrium strategies. J. Theor. Biol. 76, 109–123.
Rood, J. P. (1980). Mating relationships and breeding suppression in the dwarf mongoose. Anim. Behav. 28, 143–150.
Thomas, B. and H. J. Pohley (1981). ESS theory for finite populations. Biosystems 13, 211–221.
Vehrencamp, S. L. (1983). A model for the evolution of despotic versus egalitarian societies. Anim. Behav. 31, 667–682.
Vehrencamp, S. L., R. R. Koford and B. S. Bowen (1988). in Reproductive Success, T. H. Clutton-Brock (Ed.), University Chicago Press, pp. 291–304.
von Neumann, J. and O. Morgenstern (1944). Theory of Games and Economic Behaviour, Princeton, NJ: Princeton University Press.
Author information
Authors and Affiliations
Additional information
M. Broom is also a member of the Centre for the Study of Evolution at the University of Sussex.
Rights and permissions
About this article
Cite this article
Broom, M., Cannings, C. & Vickers, G.T. Evolution in knockout conflicts: The fixed strategy case. Bull. Math. Biol. 62, 451–466 (2000). https://doi.org/10.1006/bulm.1999.0161
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1006/bulm.1999.0161