TITLE: Dynamic policies to learn and earn in a customized pricing context

SPEAKER: J. Michael Harrison

ABSTRACT:

Motivated
by applications in financial services, we consider the following customized
pricing problem.  A seller of some good
or service (like auto loans or small business loans) confronts a sequence of
potential customers numbered 1, 2, … , T.  These customers are drawn at random from a
population characterized by a price-response function r(p).  That is, if the seller offers price p, then the probability of a successful
sale is r(p).  The profit realized from
a successful sale is p(p) = p – c, where c > 0 is known. 

 If
the price-response function r(×) were also known, then
the problem of finding a price p* to
maximize r(p)p(p) would be simple, and the
seller would offer price p* to each
of the T customers.  We consider the more complicated case where r(×) is fixed but initially unknown: roughly speaking, the seller wants to
choose prices sequentially so as to maximize the total profit earned from the T potential customers; each successive
choice involves a trade-off between refined estimation of the unknown
price-response function (learning) and immediate profit (earning).

 *
Joint work with Bora Keskin and Assaf Zeevi