Searching for the Best Offer when the Distribution of Offers is Truly Unknown

Rank-oriented models of search have not found their recognition in the economics of information literature so far. Despite the title of Rothschilds’s well-known ariticle on “Searching for the Lowest Price when the Distribution of Prices is Unknown” [10] he only considers multinomially distributed prices. We shall consider the case when no distribution is known and we have to use the relative ranks of the offers observed in guiding the search process. In sampling without recall we consider two extreme cases: it is possible to remember all offers observed so far in sorting order (unlimited memory) it is possible to remember only the best offer observed so far (extremly limited memory).