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  • Hector Chade

    (Dept. of Economics, Arizona State University)

  • Lones Smith

    (Dept. of Economics, University of Michigan)

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. 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.

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File URL: http://cowles.econ.yale.edu/P/cd/d15b/d1556.pdf
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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1556.

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Length: 16 pages
Date of creation: Jan 2006
Date of revision:
Publication status: Published in Econometrica (2006), 74(5): 1293-1307
Handle: RePEc:cwl:cwldpp:1556

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Postal: Yale University, Box 208281, New Haven, CT 06520-8281 USA
Phone: (203) 432-3702
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Web page: http://cowles.econ.yale.edu/
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

Related research

Keywords: college application; submodular optimization; greedy algorithm; directed search;

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References

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  1. Albrecht, James & Gautier, Pieter & Vroman, Susan, 2003. "Equilibrium Directed Search with Multiple Applications," IZA Discussion Papers 719, Institute for the Study of Labor (IZA).
  2. Milgrom, P. & Shannon, C., 1991. "Monotone Comparative Statics," Papers 11, Stanford - Institute for Thoretical Economics.
  3. Hector Chade & Lones Smith, 2005. "Simultaneous Search," NajEcon Working Paper Reviews 172782000000000033, www.najecon.org.
  4. Burdett, Kenneth & Judd, Kenneth L, 1983. "Equilibrium Price Dispersion," Econometrica, Econometric Society, vol. 51(4), pages 955-69, July.
  5. Kenneth Burdett & Shouyong Shi & Randall Wright, 2001. "Pricing and Matching with Frictions," Journal of Political Economy, University of Chicago Press, vol. 109(5), pages 1060-1085, October.
  6. Goldengorin, Boris & Tijssen, Gert A. & Tso, Michael, 1999. "The maximization of submodular functions : old and new proofs for the correctness of the dichotomy algorithm," Research Report 99A17, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
  7. Weitzman, Martin L, 1979. "Optimal Search for the Best Alternative," Econometrica, Econometric Society, vol. 47(3), pages 641-54, May.
  8. George J. Stigler, 1961. "The Economics of Information," Journal of Political Economy, University of Chicago Press, vol. 69, pages 213.
  9. Kelso, Alexander S, Jr & Crawford, Vincent P, 1982. "Job Matching, Coalition Formation, and Gross Substitutes," Econometrica, Econometric Society, vol. 50(6), pages 1483-1504, November.
  10. Hector Chade & Greg Lewis & Lones Smith, 2006. "The College Admissions Problem Under Uncertainty," 2006 Meeting Papers 125, Society for Economic Dynamics.
  11. Gul, Faruk & Stacchetti, Ennio, 1999. "Walrasian Equilibrium with Gross Substitutes," Journal of Economic Theory, Elsevier, vol. 87(1), pages 95-124, July.
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