Optimal Search for the Best Alternative

A BROAD CLASS of economic search problems can be cast in the following form. There are a number of different opportunities or sources, each yielding an unknown reward. The uncertainty about the reward from a source can be eliminated, at a fee, by searching or sampling. Each source has its own independent probability distribution for the reward, search cost, and search time. Sources are sampled sequentially, in whatever order is desired. When it has been decided to stop searching, only one opportunity is accepted, the maximum sampled reward. Under this formulation, what sequential search strategy maximizes expected present discounted value? A powerful solution concept applies to the above model. Each source is assigned a reservation price-an invariant critical number analogous to an internal rate of return. The reservation price of a source is easily computed, depends only on the features of that source, and has an intuitive economic interpretation. The selection rule is to search next that unsampled source with highest reservation price. The stopping rule is to terminate search whenever the maximum sampled reward is above the reservation price of every unsampled source. This simple characterization of an optimal policy is the basic result of the present paper. Fundamental properties are derived and interpreted.