G . Kohn and Steven Shavell
نویسنده
چکیده
The description of economic behavior as sequential decision making under uncertainty has been hampered by the limited nature of the available theoretical results. This paper tries to fill some of the gaps. In particular, the paper develops some basic results for the problem of search. We present a general formulation of the search problem in Section 2. Search is seen as sequential sampling from a population X. The sample points xt could be prices in different stores for a given good, the qualities of nonhomogeneous goods, job offers, or bids for an asset, to name several obvious examples; for concreteness, we occasionally refer to a searching consumer. Our results apply to the general search problem and in no way depend on any given interpretation 01 example. An individual engaged in search is assumed to have a probability distribution over X. This might be an “‘objective” distribution known with certainty or an uncertain prior that will be revised in the light of additional sample information. We show that in very general circumstances the optimal decision rule of an expected utility maximizer takes the form of a swifchpoint level of utility s. If the utility of the best xt available so far is higher than s, the search will end; otherwise it will continue. As new samples are drawn, s may change. The switchpoint can in general be characterized only in terms of a functional equation that is impossible to solve explicitly. Therefore, in Section 3 we develop calculable and easily interpretable upper and lower bounds for the switchpoint. In so doing we show that the switchpoint when the distribution is not known with certainty is at least as great as that when the distribution is known with certainty. This is because in the former case the potential benefits of continued search include the acquisition of additional information about the distribution. In most real situa-
منابع مشابه
Contractual Holdup and Legal Intervention S. Shavell 3/5/08 Contracts, Holdup, and Legal Intervention
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