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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.

Suggested Citation

  • Matthijs van Veelen, 2010. "But Some Neutrally Stable Strategies are More Neutrally Stable than Others," Tinbergen Institute Discussion Papers 10-033/1, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20100033
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    References listed on IDEAS

    as
    1. Matthijs van Veelen, 2007. "Evolution of Strategies in Repeated Games with Discounting," Tinbergen Institute Discussion Papers 06-115/1, Tinbergen Institute.
    2. Swinkels, Jeroen M., 1992. "Evolutionary stability with equilibrium entrants," Journal of Economic Theory, Elsevier, vol. 57(2), pages 306-332, August.
    3. Karl H. Schlag & Dieter Balkenborg, 2001. "Evolutionarily stable sets," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(4), pages 571-595.
    4. Fudenberg, Drew & Imhof, Lorens A., 2006. "Imitation processes with small mutations," Journal of Economic Theory, Elsevier, vol. 131(1), pages 251-262, November.
    5. 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.
    6. 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.
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    Cited by:

    1. van Veelen, Matthijs, 2012. "Robustness against indirect invasions," Games and Economic Behavior, Elsevier, vol. 74(1), pages 382-393.
    2. García, Julián & van Veelen, Matthijs, 2016. "In and out of equilibrium I: Evolution of strategies in repeated games with discounting," Journal of Economic Theory, Elsevier, vol. 161(C), pages 161-189.

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    More about this item

    Keywords

    Robustness against indirect invasions; neutrally stable strategy; evolutionarily stable strategy; extensive form game;
    All these keywords.

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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