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Dynamics in stochastic evolutionary models

Author

Listed:
  • Levine, David Knudsen

    (Department of Economics, Washington University in St. Louis and European University Institute)

  • Modica, Salvatore

    (Department of Economics, Universita di Palermo)

Abstract

We characterize transitions between stochastically stable states and relative ergodic probabilities in the theory of the evolution of conventions. We give an application to the fall of hegemonies in the evolutionary theory of institutions and conflict and illustrate the theory with the fall of the Qing Dynasty and rise of Communism in China.

Suggested Citation

  • Levine, David Knudsen & Modica, Salvatore, 2016. "Dynamics in stochastic evolutionary models," Theoretical Economics, Econometric Society, vol. 11(1), January.
    • Handle: RePEc:the:publsh:1978
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    References listed on IDEAS

    as
    1. Glenn Ellison, 2000. "Basins of Attraction, Long-Run Stochastic Stability, and the Speed of Step-by-Step Evolution," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 67(1), pages 17-45.
    2. Ellison, Glenn, 1993. "Learning, Local Interaction, and Coordination," Econometrica, Econometric Society, vol. 61(5), pages 1047-1071, September.
    3. Kevin Hasker, 2014. "The Emergent Seed: A Representation Theorem for Models of Stochastic Evolution and two formulas for Waiting Time," Levine's Working Paper Archive 786969000000000954, David K. Levine.
    4. Kreindler, Gabriel E. & Young, H. Peyton, 2013. "Fast convergence in evolutionary equilibrium selection," Games and Economic Behavior, Elsevier, vol. 80(C), pages 39-67.
    5. Blume, Lawrence E., 2003. "How noise matters," Games and Economic Behavior, Elsevier, vol. 44(2), pages 251-271, August.
    6. Kandori, Michihiro & Mailath, George J & Rob, Rafael, 1993. "Learning, Mutation, and Long Run Equilibria in Games," Econometrica, Econometric Society, vol. 61(1), pages 29-56, January.
    7. David K Levine & Salvatore Modica, 2013. "Conflict, Evolution, Hegemony, and the Power of the State," Levine's Working Paper Archive 786969000000000692, David K. Levine.
    8. Binmore, Ken & Samuelson, Larry, 1997. "Muddling Through: Noisy Equilibrium Selection," Journal of Economic Theory, Elsevier, vol. 74(2), pages 235-265, June.
    9. Cui, Zhiwei & Zhai, Jian, 2010. "Escape dynamics and equilibria selection by iterative cycle decomposition," Journal of Mathematical Economics, Elsevier, vol. 46(6), pages 1015-1029, November.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Block, Juan I. & Fudenberg, Drew & Levine, David K., 2019. "Learning dynamics with social comparisons and limited memory," Theoretical Economics, Econometric Society, vol. 14(1), January.
    2. Cui, Zhiwei, 2023. "Linking friction, social coordination and the speed of evolution," Games and Economic Behavior, Elsevier, vol. 140(C), pages 410-430.
    3. Dziubiński, Marcin & Goyal, Sanjeev & Minarsch, David E.N., 2021. "The strategy of conquest," Journal of Economic Theory, Elsevier, vol. 191(C).
    4. Juan I Block & Drew Fudenberg & David K Levine, 2017. "Learning Dynamics Based on Social Comparisons," Levine's Working Paper Archive 786969000000001375, David K. Levine.
    5. David K Levine & Salvatore Modica, 2020. "State Power and Conflict Driven Evolution," Levine's Working Paper Archive 11694000000000014, David K. Levine.
    6. Bilancini, Ennio & Boncinelli, Leonardo & Marcos-Prieto, Pablo, 2024. "Conflict initiation function shapes the evolution of persistent outcomes in group conflict," European Economic Review, Elsevier, vol. 161(C).
    7. David K Levine & Salvatore Modica, 2016. "An Evolutionary Model of Intervention and Peace," Levine's Bibliography 786969000000001391, UCLA Department of Economics.
    8. David K Levine & Salvatore Modica, 2022. "Survival of the Weakest: Why the West Rules," Levine's Working Paper Archive 786969000000001458, David K. Levine.
    9. Levine, David K. & Modica, Salvatore, 2022. "Survival of the Weakest: Why the West Rules," Journal of Economic Behavior & Organization, Elsevier, vol. 204(C), pages 394-421.
    10. Jonathan Newton, 2018. "Evolutionary Game Theory: A Renaissance," Games, MDPI, vol. 9(2), pages 1-67, May.
    11. Zhang Xu & Wei Zhao, 2024. "On Mechanism Underlying Algorithmic Collusion," Papers 2409.01147, arXiv.org.
    12. Drew Fudenberg & David K Levine, 2016. "Whither Game Theory?," Levine's Working Paper Archive 786969000000001307, David K. Levine.

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    More about this item

    Keywords

    Evolution; conventions; markov chains; state power;
    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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