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But Some Neutrally Stable Strategies are More Neutrally Stable than Others

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  • Matthijs van Veelen

    (University of Amsterdam)

Abstract

For games in which there is no evolutionarily stable strategy, it can be useful to look for neutrally stable ones. In extensive form games for instance there is typically no evolutionary stable strategy, while there may very well be a neutrally stable one. Such 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. Robustness against indirect invasions turns out to come with a very natural setwise generalisation of evolutionary stability; we prove that if a strategy is robust against indirect invasions, then this strategy and its (indirect) neutral mutants form a set that is asymptotically stable in the replicator dynamics.

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Bibliographic Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 10-033/1.

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Date of creation: 19 Mar 2010
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Handle: RePEc:dgr:uvatin:20100033

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Web page: http://www.tinbergen.nl

Related research

Keywords: Robustness against indirect invasions; neutrally stable strategy; evolutionarily stable strategy; extensive form game;

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  1. Matthijs van Veelen, 2007. "Evolution of Strategies in Repeated Games with Discounting," Tinbergen Institute Discussion Papers 06-115/1, Tinbergen Institute.
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Cited by:
  1. Matthijs van Veelen & Julian Garcia, 2010. "In and Out of Equilibrium: Evolution of Strategies in Repeated Games with Discounting," Tinbergen Institute Discussion Papers 10-037/1, Tinbergen Institute.
  2. van Veelen, Matthijs, 2012. "Robustness against indirect invasions," Games and Economic Behavior, Elsevier, vol. 74(1), pages 382-393.

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