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Paul Samuelson's critique and equilibrium concepts in evolutionary game theory

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  • Reinoud Joosten

Abstract

We present two new notions of evolutionary stability, the truly evolutionarily stable state (TESS) and the generalized evolutionarily stable equilibrium (GESE). The GESE generalizes the evolutionarily stable equilibrium (ESE) of Joosten [1996]. An ESE attracts all nearby trajectories monotonically, i.e., the Euclidean distance decreasing steadily in time. For a GESE this property should holds for at least one metric. The TESS generalizes the evolutionarily stable strategy (ESS) of Maynard Smith & Price [1973]. A TESS attracts nearby trajectories too, but the behavior of the dynamics nearby must be similar to the behavior of the replicator dynamics near an ESS. Both notions are defned on the dynamics and immediately imply asymptotical stability for the dynamics at hand, i.e., the equilibrium attracts all trajectories sufficiently nearby. We consider this the relevant and conceptually right approach in defining evolutionary equilibria, rather than defining a static equilibrium notion and search for appropriate dynamics guaranteeing its dynamic stability. Moreover, the GESE and the TESS take similar positions as the ESE and ESE do in relation to other equilibrium and fixed point concepts in general.

Suggested Citation

  • Reinoud Joosten, 2009. "Paul Samuelson's critique and equilibrium concepts in evolutionary game theory," Papers on Economics and Evolution 2009-16, Philipps University Marburg, Department of Geography.
  • Handle: RePEc:esi:evopap:2009-16
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    References listed on IDEAS

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    More about this item

    Keywords

    evolutionary stability; evolutionary game theory Length 27 pages;

    JEL classification:

    • A12 - General Economics and Teaching - - General Economics - - - Relation of Economics to Other Disciplines
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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