Learning with Finite Memory

Abstract:

The talk will focus on the learning problem of a set of agents observing the decisions of a fixed number of their immediate predecessors as well as their private signal. The problem will be analysed from two perspectives. Firstly, we study the engineered version of the prob- lem where the main question is the existence of a decision rule for which learning is achieved as the number of agents grows to infinity. For the case of bounded private beliefs we show that almost sure learning cannot occur but we provide a decision rule that achieves learn- ing in probability when agents are observing two or more of their immediate predecessors. Secondly, we study the social version of the problem where agents are making a decision maximizing the discounted sum of the error probabilities of the future agents. We analyse the perfect Bayesian equilibrium of the dynamic game where each agent sequentially receives a signal about an underlying state of the world, observes a number of the past actions and chooses one of two possible actions. Surprisingly enough for all discount factors bounded away from zero and one learning in probability does not occur under bounded private beliefs.

Biography:

Kimon Drakopoulos received his B.S.E. degree in Electrical Engineering from the National Technical University of Athens in 2009. He is currently a Ph.D student in the Lab- oratory for Information and Decision Systems under the supervision of Asuman Ozdaglar and John Tsitsiklis.