Robustness against indirect invasions
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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References listed on IDEAS
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- Matthijs van Veelen, 2010. "But Some Neutrally Stable Strategies are More Neutrally Stable than Others," Tinbergen Institute Discussion Papers 10-033/1, Tinbergen Institute.
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- Fudenberg, Drew & Imhof, Lorens A., 2006. "Imitation processes with small mutations," Journal of Economic Theory, Elsevier, vol. 131(1), pages 251-262, November.
- Drew Fudenberg & Lorens A. Imhof, 2004. "Imitation Processes with Small Mutations," Harvard Institute of Economic Research Working Papers 2050, Harvard - Institute of Economic Research.
- Fudenberg, Drew & Imhof, Lorens, 2006. "Imitation Processes with Small Mutations," Scholarly Articles 3190369, Harvard University Department of Economics.
- 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.
- 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. Full references (including those not matched with items on IDEAS)
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