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On the Evolution of Continuous Types Under Replicator and Gradient Dynamics: Two Examples

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  • Jean Paul Rabanal

    (Pettengill Hall)

Abstract

This paper illustrates techniques for assessing the dynamic stability of games where a continuum of types might be present by re-analyzing two models under incomplete information, the Lohman et al. (Unpublished manuscript, 2001) public goods game and the Kopel et al. (J Econ Dyn Control 48:394–409, 2014) Cournot duopoly game. The evolution of continuous types follows either replicator dynamics Oechssler and Riedel (Econ Theory 17:141–162, 2001; J Econ Theory 107:223–252 2002) or gradient dynamics Friedman and Ostrov (J Math Econ 46:691–707, 2010; J Econ Theory 148:743–777, 2013). The techniques rely on a system of partial differential equations. Numerical solutions obtained through replicator and gradient dynamics highlight the differences and the similarities that arise under both approaches. In the public goods game, the dynamic system affects the stationary distribution of types while in the Cournot duopoly model, the types evolve to a single mass point regardless of the dynamics used. Lastly, these techniques allow us to endogenize the distribution of player types.

Suggested Citation

  • Jean Paul Rabanal, 2017. "On the Evolution of Continuous Types Under Replicator and Gradient Dynamics: Two Examples," Dynamic Games and Applications, Springer, vol. 7(1), pages 76-92, March.
    • Handle: RePEc:spr:dyngam:v:7:y:2017:i:1:d:10.1007_s13235-015-0164-0
    DOI: 10.1007/s13235-015-0164-0
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Philip J. Grossman & Youngseok Park & Jean Paul Rabanal & Olga A. Rud, 2019. "Gender differences in an endogenous timing conflict game," Working Papers 141, Peruvian Economic Association.
    2. Domenico De Giovanni & Fabio Lamantia, 2017. "Evolutionary dynamics of a duopoly game with strategic delegation and isoelastic demand," Journal of Evolutionary Economics, Springer, vol. 27(5), pages 877-903, November.
    3. Kopel, Michael & Lamantia, Fabio, 2018. "The persistence of social strategies under increasing competitive pressure," Journal of Economic Dynamics and Control, Elsevier, vol. 91(C), pages 71-83.
    4. Rabanal, Jean Paul & Lee, Dongwook, 2017. "On the dynamic stability of a price dispersion model using gradient dynamics," Journal of Economic Dynamics and Control, Elsevier, vol. 84(C), pages 32-42.
    5. Fulei Shi & Chuansheng Wang & Cuiyou Yao, 2022. "A New Evolutionary Game Analysis for Industrial Pollution Management Considering the Central Government’s Punishment," Dynamic Games and Applications, Springer, vol. 12(2), pages 677-688, June.
    6. Lotito, Gianna & Migheli, Matteo & Ortona, Guido, 2019. "Some Experimental Evidence on Type Stability and Response Times," Department of Economics and Statistics Cognetti de Martiis. Working Papers 201919, University of Turin.

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    More about this item

    Keywords

    Population games; Evolutionary dynamics; Corporate social responsibility; Mixed oligopoly; Public goods;
    All these keywords.

    JEL classification:

    • 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
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets
    • L21 - Industrial Organization - - Firm Objectives, Organization, and Behavior - - - Business Objectives of the Firm
    • M14 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Administration - - - Corporate Culture; Diversity; Social Responsibility
    • H41 - Public Economics - - Publicly Provided Goods - - - Public Goods

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