Abstract
The implications of evolutionarily stable behavior in finite populations have recently been explored for a variety of aggregative games. This note proves an intimate relationship between quasi-submodularity and global evolutionary stability of strategies for these games, which – apart from being of independent interest – accounts for a number of results obtained in the recent literature: we show that any evolutionarily stable strategy of a quasi-submodular aggregative game must also be globally stable. That is, if one mutant cannot successfully invade a population, any number of mutants can do so even less
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References
Alós-Ferrer C., Ania A. (2005). The evolutionary stability of perfectly competitive behavior. Econ Theory 26(3):497–516
Ellison G. (2000). Basins of attraction, long-run stochastic stability, and the speed of step-by-step evolution. Rev Econ Stud 67:17–45
Hehenkamp B., Leininger W., Possajennikov A. (2004). Evolutionary equilibrium in Tullock contests: spite and overdissipation. Eur J Polit Econ 20:1045–1057
Leininger W. Contests over public goods: evolutionarily stability and the free-rider problem. CESifo Working Paper No. 713 (2002)
Leininger W. (2003). On evolutionarily stable behavior in contests. Econ Gov 4:177–186
Maynard Smith J. (1974). Evolution and the theory of games. Cambridge University Press, Cambridge
Nowak M.A., Sigmund K. (2004). Evolutionary dynamics of biological games. Science 303:793–799
Possajennikov A. (2003). Evolutionary foundations of aggregate-taking behavior. Econ Theory 21: 921–928
Schaffer M. (1988). Evolutionarily stable strategies for a finite population and a variable contest size. J Theoretical Biol 132:469–478
Schaffer M. (1989). Are profit-maximizers the best survivers? J Econ Behav Organ 12:29–45
Schenk-Hoppé R. (2000). The evolution of Walrasian behavior in oligopolies. J Math Econ 33:35–55
Topkis D. (1998). Supermodularity and complementarity. Princeton University Press, Princeton
Tullock G. (1980). Efficient rent-seeking. In: Buchanan J., Tollison R., Tullock G. (eds.) Towards a theory of the rent-seeking society. A&M University Press, Texas, pp. 3–15
Vega-Redondo F. (1997). The evolution of Walrasian behavior. Econometrica 65:375–384
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The author is grateful to Ana Ania and Carlos Alōs-Ferrer for comments on an earlier version
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Leininger, W. Fending off one means fending off all: evolutionary stability in quasi-submodular aggregative games. Economic Theory 29, 713–719 (2006). https://doi.org/10.1007/s00199-005-0027-9
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DOI: https://doi.org/10.1007/s00199-005-0027-9