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Simultaneous Search

Author

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  • Lones Smith
  • Hector Chade

Abstract

We introduce and solve a new class of static portfolio choice problems, where only the best realized alternative matters. A decision maker must simultaneously choose among independent ranked options, and the better alternatives have a lower chance of panning out. Each choice is costly, and just one option may be exercised. This often emerges in practice: (i) A student must make a costly and simultaneous application to many colleges, and is accepted with smaller chances by the better schools; (ii) An economics department must decide which of several PhD job candidates to fly out, and the better recruits will be available with smaller probability. We show that this problem entails maximizing a submodular function of finite sets --- which is NP hard in general. Still, we develop a marginal improvement algorithm that produces the optimal set in a quadratic number of steps. Applying it, we then show that the optimal choices are less risky than the sequentially optimal ones in Weitzman (1979), but riskier than the best singleton college choices. We also give practical rules of thumb, such as: (i) don't insure, choosing a safety school; instead, take risks; (ii) apply to an upwardly diverse portfolio of schools

Suggested Citation

  • Lones Smith & Hector Chade, 2004. "Simultaneous Search," 2004 Meeting Papers 25, Society for Economic Dynamics.
  • Handle: RePEc:red:sed004:25
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    References listed on IDEAS

    as
    1. James Albrecht & Pieter A. Gautier & Susan Vroman, 2006. "Equilibrium Directed Search with Multiple Applications," Review of Economic Studies, Oxford University Press, vol. 73(4), pages 869-891.
    2. Stigler, George J., 2011. "Economics of Information," Economic Policy, Russian Presidential Academy of National Economy and Public Administration, vol. 5, pages 35-49.
    3. Hector Chade & Lones Smith, 2006. "Simultaneous Search," Econometrica, Econometric Society, vol. 74(5), pages 1293-1307, September.
    4. 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.
    5. Gul, Faruk & Stacchetti, Ennio, 1999. "Walrasian Equilibrium with Gross Substitutes," Journal of Economic Theory, Elsevier, vol. 87(1), pages 95-124, July.
    6. Burdett, Kenneth & Judd, Kenneth L, 1983. "Equilibrium Price Dispersion," Econometrica, Econometric Society, vol. 51(4), pages 955-969, July.
    7. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-180, January.
    8. Weitzman, Martin L, 1979. "Optimal Search for the Best Alternative," Econometrica, Econometric Society, vol. 47(3), pages 641-654, May.
    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.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    search; submodular function;

    JEL classification:

    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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