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Games 2010, 1(4), 438-458; doi:10.3390/g1040438

Article

Bayesian Social Learning with Local Interactions

Antonio Guarino ¹  and Antonella Ianni ^2,*

¹ Department of Economics ELSE, University College London, London WC1E 6BT, UK ² Economic Division, School of Social Sciences, University of Southampton, Southampton SO17 1BJ, UK

* Author to whom correspondence should be addressed.

Received: 8 September 2010 / Accepted: 2 October 2010 / Published: 20 October 2010

(This article belongs to the Special Issue Social Networks and Network Formation)

Download PDF Full-Text [331 KB, uploaded 20 October 2010 15:19 CEST]

Abstract: We study social learning in a large population of agents who only observe the actions taken by their neighbours. Agents have to choose one, out of two, reversible actions, each optimal in one, out of two, unknown states of the world. Each agent chooses rationally, on the basis of private information and of the observation of his neighbours’ actions. Agents can repeatedly update their choices at revision opportunities that they receive in a random sequential order. We show that if agents receive equally informative signals and observe both neighbours, then actions converge exponentially fast to a configuration where some agents are permanently wrong. In contrast, if agents are unequally informed (in that some agents receive a perfectly informative signal and others are uninformed) and observe one neighbour only, then everyone will eventually choose the correct action. Convergence, however, obtains very slowly, at rate √t.

Keywords: social learning; Bayesian learning; local informational externalities; path dependence; consensus; clustering; convergence rates

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