Expected value maximizing sequential search rules can be expressed in terms of reservation values. In search with learning the reservation value at any stage of the search is unknown until that stage is reached. Thus calculating ex ante (and subsequent) probabilities of search duration and the offer accepted is difficult if these probabilities are expressed in terms of reservation values. This paper shows, for a wide class of learning procedures, how re-expressing these probabilities in terms of fixed points allows their direct calculation and, thereby, calculation of the expected value of adaptive search. Examples and comparative statics results are presented.

[This paper presents general results on the existence and properties of expected-utility-maximizing search rules for problems in which searchers may choose both the number of periods in which samples are taken and the size of the sample taken in each period. These rules include fixed-sample-size rules and sequential rules as special cases. Also presented are conditions sufficient for sequential and fixed-sample-size rules to be optimal.]