An example of non-Martingale learning
Lones Smith, Peter Birch Sørensen · DSpace@MIT (Massachusetts Institute of Technology) · 1994
This paper abandons the universal assumption in models of observational learning that individuals can perfectly observe the order of past decisions.Only a worked example so far, we show that complete learning obtains under the same conditions as before.We try to underscore that the resulting analysis in no way exploits any martingaleswhich have been the lifeblood of optimal learning theory until now."This is very preliminary and incomplete, and only a note in its present form.The authors solely wish to record the example that will be the basis for a paper once we figure out exactly what is happening.When completed, this paper will supersede "Error Persistence, and Experiential versus Observational Learning," which was presented on the Review of Economic Studies Tour of London, Brussels, ajid Tel Aviv in 1991.The reincarnation of this paper as joint work partially reflects some especially fruitful conversations with Mathias Dewatripont and Guy Laroque.^The authors wish to thank Marco Ottaviani, and participants at the MIT theory lunch for their comments.We are grateful to Robert Shimer for pointing out that we had enough equations to find closed form solutions for the distribution of our random variables, and for supplying a simulation on Mathematica.All errors remain our responsibility.