COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY

Box 208281
New Haven, CT 06520-8281

COWLES FOUNDATION DISCUSSION PAPER NO. 1556

Simultaneous Search

Hector Chade
Department of Economics, Arizona State University
Lones Smith
Department of Economics, University of Michigan

January 2006

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.

We show that a greedy algorithm finds the optimal set. The optimal choices are "less aggressive'' than the sequentially optimal ones, but "more aggressive'' than the best singletons. The optimal set in general contains gaps. We provide a comparative static on the chosen set.

Keywords: College application, Submodular optimization, Greedy algorithm, Directed search

JEL Classification: C61, D83, J64