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Robustness against indirect invasions

  • van Veelen, Matthijs

Games that have no evolutionarily stable strategy may very well have neutrally stable ones. (Neutrally stable strategies are also known as weakly evolutionarily stable strategies.) Such neutrally, but not evolutionarily stable strategies can however still be relatively stable or unstable, depending on whether or not the neutral mutants it allows for – which by definition do not have a selective advantage themselves – can open doors for other mutants that do have a selective advantage. This paper defines robustness against indirect invasions in order to be able to discern between those two very different situations. Being robust against indirect invasions turns out to be equivalent to being an element of a minimal ES set, where this minimal ES set is the set that consists of this strategy and its (indirect) neutral mutants. This is useful, because we know that ES sets are asymptotically stable in the replicator dynamics.

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File URL: http://www.sciencedirect.com/science/article/pii/S0899825611000960
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Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 74 (2012)
Issue (Month): 1 ()
Pages: 382-393

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Handle: RePEc:eee:gamebe:v:74:y:2012:i:1:p:382-393
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622836

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  1. Swinkels, J., 1991. "Evolutionary Stability with Equilibrium Entrants," Papers 9, Stanford - Institute for Thoretical Economics.
  2. Matthijs van Veelen, 2010. "But Some Neutrally Stable Strategies are More Neutrally Stable than Others," Tinbergen Institute Discussion Papers 10-033/1, Tinbergen Institute.
  3. Fudenberg, Drew & Imhof, Lorens, 2006. "Imitation Processes with Small Mutations," Scholarly Articles 3190369, Harvard University Department of Economics.
  4. Swinkels, Jeroen M., 1992. "Evolution and strategic stability: From maynard smith to kohlberg and mertens," Journal of Economic Theory, Elsevier, vol. 57(2), pages 333-342, August.
  5. Matthijs van Veelen, 2010. "But Some Neutrally Stable Strategies are More Neutrally Stable than Others," Tinbergen Institute Discussion Papers 10-033/1, Tinbergen Institute.
  6. Balkenborg, Dieter & Schlag, Karl H., 2007. "On the evolutionary selection of sets of Nash equilibria," Journal of Economic Theory, Elsevier, vol. 133(1), pages 295-315, March.
  7. Karl H. Schlag & Dieter Balkenborg, 2001. "Evolutionarily stable sets," International Journal of Game Theory, Springer, vol. 29(4), pages 571-595.
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