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Naive learning in social networks: Imitating the most successful neighbor

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  • Tsakas, Nikolas

Abstract

This paper considers a model of observational learning in social networks. Every period, the agents observe the actions of their neighbors and their realized outcomes, and they imitate the most successful. First, we study the case where the network has finite population and we show that, regardless of the structure, the population converges to a monomorphic steady state, i.e. where every agent chooses the same action. Subsequently, we extend our analysis to infinitely large networks and we differentiate the cases where agents have bounded neighborhoods, with those where they do not. Under bounded neighborhoods, an action is diffused to the whole population if it is the only one initially chosen by infinitely many agents. If there exist more than one such actions, we provide an additional sufficient condition in the payoff structure, which ensures convergence for any network. Without the assumption of bounded neighborhoods, we show that an action can survive even if it is initially chosen by a single agent and also that a network can be in steady state without this being monomorphic.

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File URL: http://mpra.ub.uni-muenchen.de/45210/
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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 37796.

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Date of creation: 23 Mar 2012
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Handle: RePEc:pra:mprapa:37796

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Keywords: Social Networks; Learning; Diffusion; Imitation;

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  1. Eddie Dekel & Drew Fudenberg & David K. Levine, 2000. "Learning to Play Bayesian Games," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 1322, Northwestern University, Center for Mathematical Studies in Economics and Management Science, revised Jul 2001.
  2. Abhijit Banerjee & Drew Fudenberg, 2010. "Word of Mouth Learning," Levine's Working Paper Archive 723, David K. Levine.
  3. Jose Apesteguia & Steffen Huck & Jörg Oechssler, 2005. "Imitation - Theory and Experimental Evidence -," Working Papers, University of Heidelberg, Department of Economics 0419, University of Heidelberg, Department of Economics, revised Apr 2005.
  4. Alós-Ferrer, Carlos & Weidenholzer, Simon, 2008. "Contagion and efficiency," Journal of Economic Theory, Elsevier, Elsevier, vol. 143(1), pages 251-274, November.
  5. Timothy G. Conley & Christopher R. Udry, 2005. "Learning about a new technology: pineapple in Ghana," Proceedings, Federal Reserve Bank of San Francisco, Federal Reserve Bank of San Francisco.
  6. Fernando Vega-Redondo, 1997. "The Evolution of Walrasian Behavior," Econometrica, Econometric Society, Econometric Society, vol. 65(2), pages 375-384, March.
  7. Ellison, Glenn & Fudenberg, Drew, 1992. "Rules of Thumb for Social Learning," IDEI Working Papers, Institut d'Économie Industrielle (IDEI), Toulouse 17, Institut d'Économie Industrielle (IDEI), Toulouse.
  8. Drew Fudenberg & David K. Levine, 1996. "The Theory of Learning in Games," Levine's Working Paper Archive 624, David K. Levine.
  9. Ellison, Glenn & Fudenberg, Drew, 1995. "Word-of-Mouth Communication and Social Learning," The Quarterly Journal of Economics, MIT Press, MIT Press, vol. 110(1), pages 93-125, February.
  10. Schlag, Karl H., 1998. "Why Imitate, and If So, How?, : A Boundedly Rational Approach to Multi-armed Bandits," Journal of Economic Theory, Elsevier, Elsevier, vol. 78(1), pages 130-156, January.
  11. Schlag, Karl H., 1999. "Which one should I imitate?," Journal of Mathematical Economics, Elsevier, vol. 31(4), pages 493-522, May.
  12. Constanza Fosco & Friederike Mengel, 2009. "Cooperation through Imitation and Exclusion in Networks," Working Papers, Fondazione Eni Enrico Mattei 2009.37, Fondazione Eni Enrico Mattei.
  13. Bala, Venkatesh & Goyal, Sanjeev, 1998. "Learning from Neighbours," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 65(3), pages 595-621, July.
  14. Gale, Douglas & Kariv, Shachar, 2003. "Bayesian learning in social networks," Games and Economic Behavior, Elsevier, Elsevier, vol. 45(2), pages 329-346, November.
  15. Eshel, Ilan & Samuelson, Larry & Shaked, Avner, 1998. "Altruists, Egoists, and Hooligans in a Local Interaction Model," American Economic Review, American Economic Association, American Economic Association, vol. 88(1), pages 157-79, March.
  16. Josephson, Jens & Matros, Alexander, 2004. "Stochastic imitation in finite games," Games and Economic Behavior, Elsevier, Elsevier, vol. 49(2), pages 244-259, November.
  17. Banerjee, Abhijit V, 1992. "A Simple Model of Herd Behavior," The Quarterly Journal of Economics, MIT Press, MIT Press, vol. 107(3), pages 797-817, August.
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