Stability of the Replicator Equation for a Single-Species with a Multi-Dimensional Continuous Trait Space
The replicator equation model for the evolution of individual behaviors in a single-species with a multi-dimensional continuous trait space is developed as a dynamics on the set of probability measures. Stability of monomorphisms in this model using the weak topology is compared to more traditional methods of adaptive dynamics. For quadratic fitness functions and initial normal trait distributions, it is shown that the multi-dimensional CSS (Continuously Stable Strategy) of adaptive dynamics is often relevant for predicting stability of the measure-theoretic model but may be too strong in general. For general fitness functions and trait distributions, the CSS is related to dominance solvability which can be used to characterize local stability for a large class of trait distributions that have no gaps in their supports whereas the stronger NIS (Neighborhood Invader Strategy) concept is needed if the supports are arbitrary.
|Date of creation:||Apr 2005|
|Date of revision:|
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- Alos-Ferrer, Carlos & Ania, Ana B., 2001. "Local equilibria in economic games," Economics Letters, Elsevier, vol. 70(2), pages 165-173, February.
- Samuelson, L. & Zhang, J., 1990.
"Evolutionary Stability In Symmetric Games,"
90-24, Wisconsin Madison - Social Systems.
- Aviad Heifetz & Chris Shannon & Yossi Spiegel, 2003.
"What to Maximize If You Must,"
Game Theory and Information
- Aviad Heifetz & Chris Shannon & Yossi Spiegel, 2004. "What to Maximize if You Must," Discussion Papers 1414, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Chris Shannon, 2003. "What to Maximize if You Must," Theory workshop papers 658612000000000044, UCLA Department of Economics.
- HEIFETZ, Aviad & SHANNON, Chris & SPIEGEL, Yossi, 2003. "What to maximize if you must," CORE Discussion Papers 2003047, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Cressman, Ross, 2005. "Stability of the replicator equation with continuous strategy space," Mathematical Social Sciences, Elsevier, vol. 50(2), pages 127-147, September.
- JÃrg Oechssler & Frank Riedel, 2001.
"Evolutionary dynamics on infinite strategy spaces,"
Springer;Society for the Advancement of Economic Theory (SAET), vol. 17(1), pages 141-162.
- Joerg Oechssler & Frank Riedel, 1998. "Evolutionary Dynamics on Infinite Strategy Spaces," Game Theory and Information 9805002, EconWPA, revised 12 May 1998.
- Oechssler, Jörg & Riedel, Frank, 1998. "Evolutionary dynamics on infinite strategy spaces," SFB 373 Discussion Papers 1998,68, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
- Oechssler, Joerg & Frank Riedel, 1999. "Evolutionary Dynamics on Infinite Strategy Spaces," Discussion Paper Serie A 606, University of Bonn, Germany.
- P. Marrow & U. Dieckmann & R. Law, 1996. "Evolutionary Dynamics of Predator-Prey Systems: An Ecological Perspective," Working Papers wp96002, International Institute for Applied Systems Analysis.
- Jörg Oechssler & Frank Riedel, 2000.
"On the Dynamic Foundation of Evolutionary Stability in Continuous Models,"
Bonn Econ Discussion Papers
bgse7_2000, University of Bonn, Germany.
- Oechssler, Jorg & Riedel, Frank, 2002. "On the Dynamic Foundation of Evolutionary Stability in Continuous Models," Journal of Economic Theory, Elsevier, vol. 107(2), pages 223-252, December.
- Oechssler, Jörg & Riedel, Frank, 2000. "On the dynamic foundation of evolutionary stability in continuous models," SFB 373 Discussion Papers 2000,73, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
- Joerg Oechssler & Frank Riedel, 2000. "On the Dynamic Foundation of Evolutionary Stability in Continuous Models," Game Theory and Information 0004004, EconWPA.
- Moulin, Herve, 1984. "Dominance solvability and cournot stability," Mathematical Social Sciences, Elsevier, vol. 7(1), pages 83-102, February.
- Ross Cressman, 2003. "Evolutionary Dynamics and Extensive Form Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262033054.
- M. Doebeli & U. Dieckmann, 2000. "Evolutionary Branching and Sympatric Speciation Caused by Different Types of Ecological Interactions," Working Papers ir00040, International Institute for Applied Systems Analysis.
- Samuelson, Larry & Zhang, Jianbo, 1992. "Evolutionary stability in asymmetric games," Journal of Economic Theory, Elsevier, vol. 57(2), pages 363-391, August.
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