Simultaneous Search Simultaneous Search *

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. ∗The usage of the term ‘search’ rather than ‘choice’ here reflects a precedent set in Weitzman (1979), and in the directed search literature. We have benefited from seminars at the 2003 Midwest Economic Theory Meetings, ITAM, LBS, Penn, Duke, Michigan, Toronto Matching Conference, 2004 Society for Economic Dynamics, 2004 North American Econometric Society Meetings, 2004 Latin American Econometric Society Meetings, Yale, Texas, Stanford, and NYU. We are very grateful for research assistance of Kan Takeuchi, and the feedback of Miles Kimball, Steve Salant, and Ennio Stacchetti. Lones is grateful for the financial support of the National Science Foundation. †Email: [email protected] ‡Email: [email protected]; web: www.umich.edu/∼lones.