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Stability and strategic diffusion in networks

Author

Listed:
  • Azomahou, T.

    (UNU-MERIT)

  • Opolot, D.

    (UNU-MERIT)

Abstract

Learning and stochastic evolutionary models provide a useful framework for analyzing repeated interactions and experimentation among economic agents over time. They also provide sharp predictions about equilibrium selection when multiplicity exists. This paper defines three convergence measures, diffusion rate, expected waiting time and convergence rate, for characterizing the short-run, medium-run and long-run behavior of a typical model of stochastic evolution. We provide tighter bounds for each without making restrictive assumptions on the model and amount of noise as well as interaction structure. We demonstrate how they can be employed to characterize evolutionary dynamics for coordination games and strategic diffusion in networks. Application of our results to strategic diffusion gives insights on the role played by the network topology. For example we show how networks made up of cohesive subgroups speed up evolution between quasi-stable states while sparsely connected networks have the opposite effect of favoring almost global stability.

Suggested Citation

  • Azomahou, T. & Opolot, D., 2014. "Stability and strategic diffusion in networks," MERIT Working Papers 2014-035, United Nations University - Maastricht Economic and Social Research Institute on Innovation and Technology (MERIT).
    • Handle: RePEc:unm:unumer:2014035
    as

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    File URL: https://www.merit.unu.edu/publications/wppdf/2014/wp2014-035.pdf
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    References listed on IDEAS

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    1. Blume Lawrence E., 1995. "The Statistical Mechanics of Best-Response Strategy Revision," Games and Economic Behavior, Elsevier, vol. 11(2), pages 111-145, November.
    2. 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.
    3. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
    4. Noldeke, Georg & Samuelson, Larry, 1997. "A Dynamic Model of Equilibrium Selection in Signaling Markets," Journal of Economic Theory, Elsevier, vol. 73(1), pages 118-156, March.
    5. Michihiro, Kandori & Rob, Rafael, 1998. "Bandwagon Effects and Long Run Technology Choice," Games and Economic Behavior, Elsevier, vol. 22(1), pages 30-60, January.
    6. Huck, Steffen & Kübler, Dorothea & Weibull, Jörgen, 2012. "Social norms and economic incentives in firms," Journal of Economic Behavior & Organization, Elsevier, vol. 83(2), pages 173-185.
    7. 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.
    8. Fernando Vega-Redondo, 1997. "The Evolution of Walrasian Behavior," Econometrica, Econometric Society, vol. 65(2), pages 375-384, March.
    9. Bergin, James & Lipman, Barton L, 1996. "Evolution with State-Dependent Mutations," Econometrica, Econometric Society, vol. 64(4), pages 943-956, July.
    10. William A. Brock & Steven N. Durlauf, 2001. "Discrete Choice with Social Interactions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 68(2), pages 235-260.
    11. William H. Sandholm, 2001. "Almost global convergence to p-dominant equilibrium," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(1), pages 107-116.
    12. Lee In Ho & Szeidl Adam & Valentinyi Akos, 2003. "Contagion and State Dependent Mutations," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 3(1), pages 1-29, February.
    13. Staudigl, Mathias, 2012. "Stochastic stability in asymmetric binary choice coordination games," Games and Economic Behavior, Elsevier, vol. 75(1), pages 372-401.
    14. Ellison, Glenn, 1993. "Learning, Local Interaction, and Coordination," Econometrica, Econometric Society, vol. 61(5), pages 1047-1071, September.
    15. Edward L. Glaeser & Jose Scheinkman, 2000. "Non-Market Interactions," NBER Working Papers 8053, National Bureau of Economic Research, Inc.
    16. George A. Akerlof, 1997. "Social Distance and Social Decisions," Econometrica, Econometric Society, vol. 65(5), pages 1005-1028, September.
    17. Lelarge, Marc, 2012. "Diffusion and cascading behavior in random networks," Games and Economic Behavior, Elsevier, vol. 75(2), pages 752-775.
    18. Binmore, Ken & Samuelson, Larry, 1997. "Muddling Through: Noisy Equilibrium Selection," Journal of Economic Theory, Elsevier, vol. 74(2), pages 235-265, June.
    19. Alós-Ferrer, Carlos & Weidenholzer, Simon, 2008. "Contagion and efficiency," Journal of Economic Theory, Elsevier, vol. 143(1), pages 251-274, November.
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    More about this item

    Keywords

    Learning; innovation; evolutionary models; evolutionary games; networks; diffusion rate; convergence rate; expected waiting time;
    All these keywords.

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General
    • O33 - Economic Development, Innovation, Technological Change, and Growth - - Innovation; Research and Development; Technological Change; Intellectual Property Rights - - - Technological Change: Choices and Consequences; Diffusion Processes

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