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Robustness against indirect invasions

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  • van Veelen, Matthijs

Abstract

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.

Suggested Citation

  • van Veelen, Matthijs, 2012. "Robustness against indirect invasions," Games and Economic Behavior, Elsevier, vol. 74(1), pages 382-393.
  • Handle: RePEc:eee:gamebe:v:74:y:2012:i:1:p:382-393
    DOI: 10.1016/j.geb.2011.05.010
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    References listed on IDEAS

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    1. Swinkels, Jeroen M., 1992. "Evolutionary stability with equilibrium entrants," Journal of Economic Theory, Elsevier, vol. 57(2), pages 306-332, August.
    2. Karl H. Schlag & Dieter Balkenborg, 2001. "Evolutionarily stable sets," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(4), pages 571-595.
    3. Fudenberg, Drew & Imhof, Lorens A., 2006. "Imitation processes with small mutations," Journal of Economic Theory, Elsevier, vol. 131(1), pages 251-262, November.
    4. Matthijs van Veelen, 2010. "But Some Neutrally Stable Strategies are More Neutrally Stable than Others," Tinbergen Institute Discussion Papers 10-033/1, Tinbergen Institute.
    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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    Citations

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    Cited by:

    1. Heller, Yuval, 2017. "Instability of belief-free equilibria," Journal of Economic Theory, Elsevier, vol. 168(C), pages 261-286.
    2. repec:eee:gamebe:v:107:y:2018:i:c:p:203-219 is not listed on IDEAS
    3. Matthijs van Veelen & Julian Garcia, 2012. "In and out of Equilibrium II: Evolution in Repeated Games with Discounting and Complexity Costs," Tinbergen Institute Discussion Papers 12-089/I, Tinbergen Institute.
    4. Sandholm, William H., 2015. "Population Games and Deterministic Evolutionary Dynamics," Handbook of Game Theory with Economic Applications, Elsevier.
    5. Berger, Ulrich & Grüne, Ansgar, 2016. "On the stability of cooperation under indirect reciprocity with first-order information," Games and Economic Behavior, Elsevier, vol. 98(C), pages 19-33.
    6. Izquierdo, Luis R. & Izquierdo, Segismundo S. & Vega-Redondo, Fernando, 2014. "Leave and let leave: A sufficient condition to explain the evolutionary emergence of cooperation," Journal of Economic Dynamics and Control, Elsevier, vol. 46(C), pages 91-113.
    7. 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.

    More about this item

    Keywords

    Evolutionarily stable strategy; Neutrally stable strategy; Neutral mutant; Direct invasion; Indirect invasion; Robust against indirect invasions; Robust against equilibrium entrants; Evolutionarily stable set; Replicator dynamics; Asymptotically stable; Stochastic dynamics; Moran process; Fixation probability;

    JEL classification:

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

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