Uncertain Search: A Model of Search Among Technologies of Uncertain Values

In the standard search problem there is an infinite pool of items whose distribution of values is known. A decision maker draws an item from the pool, observes its value, and decides whether to keep it or to draw another item. He can keep only one item, and he seeks the item with the largest value. In the standard uncertainty resolution problem there is only one item, and the value of that item remains uncertain even after it is drawn. The decision maker sequentially collects observations on the value of the item and decides whether to keep the item, discard the item, or take another observation. Uncertain search marries the sequential drawing from a pool of items from the search literature with the unknown value of a drawn item from the uncertainty resolution literature. Presented in the context of technology adoption, it considers drawing from a pool of new technologies whose values remain unknown even after being drawn. The decision maker sequentially purchases information in order to Bayesianly update the prior distribution of the technology's value. After each observation, the decision maker either adopts the technology (and hence quits searching), takes another costly observation, rejects the technology and quits searching, or rejects the technology and draws the next technology from the pool for observation. The solution to this uncertain search problem is surprisingly simple: solve the version of the uncertainty resolution problem in which the return to rejecting the technology is replaced by an exit value. Then use successive approximation to find a fixed point: an exit value that equals the expected value of the uncertainty resolution problem.