Simultaneous search

Hector Chade, Lones Smith

Research output: Contribution to journalArticle

47 Scopus citations

Abstract

We introduce and solve a new class of "downward-recursive" static portfolio choice problems. An individual simultaneously chooses among ranked stochastic options, and each choice is costly. In the motivational application, just one may be exercised from those that succeed. This often emerges in practice, such as when a student applies to many colleges or when a firm simultaneously tries several technologies. We show that such portfolio choice problems quite generally entail maximizing a submodular function of finite sets - which is NP-hard in general. Still, we show that a greedy algorithm finds the optimal set, finding first the best singleton, then the best single addition to it, and so on. We show that the optimal choices are "less aggressive" than the sequentially optimal ones, but "more aggressive" than the best singletons. Also, the optimal set in general contains gaps. We provide some comparative statics results on the chosen set.

Original languageEnglish (US)
Pages (from-to)1293-1307
Number of pages15
JournalEconometrica
Volume74
Issue number5
DOIs
StatePublished - Sep 1 2006

Keywords

  • Greedy algorithm
  • Portfolio choice
  • Search
  • Submodular

ASJC Scopus subject areas

  • Economics and Econometrics

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