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Simultaneous Search

  • Lones Smith
  • Hector Chade

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

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Paper provided by Society for Economic Dynamics in its series 2004 Meeting Papers with number 25.

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Date of creation: 2004
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Handle: RePEc:red:sed004:25
Contact details of provider: Postal: Society for Economic Dynamics Christian Zimmermann Economic Research Federal Reserve Bank of St. Louis PO Box 442 St. Louis MO 63166-0442 USA
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Web page: http://www.EconomicDynamics.org/society.htm
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  1. George J. Stigler, 1961. "The Economics of Information," Journal of Political Economy, University of Chicago Press, vol. 69, pages 213.
  2. Burdett, Kenneth & Judd, Kenneth L, 1983. "Equilibrium Price Dispersion," Econometrica, Econometric Society, vol. 51(4), pages 955-69, July.
  3. Hector Chade & Greg Lewis & Lones Smith, 2006. "The College Admissions Problem Under Uncertainty," 2006 Meeting Papers 125, Society for Economic Dynamics.
  4. Milgrom, P. & Shannon, C., 1991. "Monotone Comparative Statics," Papers 11, Stanford - Institute for Thoretical Economics.
  5. Weitzman, Martin L, 1979. "Optimal Search for the Best Alternative," Econometrica, Econometric Society, vol. 47(3), pages 641-54, May.
  6. James Albrecht & Pieter Gautier, 2004. "Equilibrium Directed Search with Multiple Applications," Econometric Society 2004 Latin American Meetings 330, Econometric Society.
  7. 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.
  8. Gul, Faruk & Stacchetti, Ennio, 1999. "Walrasian Equilibrium with Gross Substitutes," Journal of Economic Theory, Elsevier, vol. 87(1), pages 95-124, July.
  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 & Lones Smith, 2005. "Simultaneous Search," NajEcon Working Paper Reviews 172782000000000033, www.najecon.org.
  11. 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).
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