03030cam a22002897 4500001000700000003000500007005001700012008004100029100002100070245013100091260006600222490004200288500001400330520174200344530006102086538007202147538003602219690007002255690015902325700002302484700001702507700002202524710004202546830007702588856003802665856003702703w14040NBER20150602204921.0150602s2008 mau||||fs|||| 000 0 eng d1 aAcemoglu, Daron.10aBayesian Learning in Social Networksh[electronic resource] /cDaron Acemoglu, Munther A. Dahleh, Ilan Lobel, Asuman Ozdaglar. aCambridge, Mass.bNational Bureau of Economic Researchc2008.1 aNBER working paper seriesvno. w14040 aMay 2008.3 aWe study the perfect Bayesian equilibrium of a model of learning over a general social network. Each individual receives a signal about the underlying state of the world, observes the past actions of a stochastically-generated neighborhood of individuals, and chooses one of two possible actions. The stochastic process generating the neighborhoods defines the network topology (social network). The special case where each individual observes all past actions has been widely studied in the literature. We characterize pure-strategy equilibria for arbitrary stochastic and deterministic social networks and characterize the conditions under which there will be asymptotic learning -- that is, the conditions under which, as the social network becomes large, individuals converge (in probability) to taking the right action. We show that when private beliefs are unbounded (meaning that the implied likelihood ratios are unbounded), there will be asymptotic learning as long as there is some minimal amount of "expansion in observations". Our main theorem shows that when the probability that each individual observes some other individual from the recent past converges to one as the social network becomes large, unbounded private beliefs are sufficient to ensure asymptotic learning. This theorem therefore establishes that, with unbounded private beliefs, there will be asymptotic learning an almost all reasonable social networks. We also show that for most network topologies, when private beliefs are bounded, there will not be asymptotic learning. In addition, in contrast to the special case where all past actions are observed, asymptotic learning is possible even with bounded beliefs in certain stochastic network topologies. aHardcopy version available to institutional subscribers. aSystem requirements: Adobe [Acrobat] Reader required for PDF files. aMode of access: World Wide Web. 7aC72 - Noncooperative Games2Journal of Economic Literature class. 7aD83 - Search • Learning • Information and Knowledge • Communication • Belief • Unawareness2Journal of Economic Literature class.1 aDahleh, Munther A.1 aLobel, Ilan.1 aOzdaglar, Asuman.2 aNational Bureau of Economic Research. 0aWorking Paper Series (National Bureau of Economic Research)vno. w14040.4 uhttp://www.nber.org/papers/w1404041uhttp://dx.doi.org/10.3386/w14040