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Simultaneous Search

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Author Info
Hector Chade () (W. P. Carey School of Business Department of Economics)
Lones Smith (University of Michigan)

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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:

• A student must make a costly and simultaneous application to many colleges, and is accepted with smaller chances by the better schools.

• 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 such portfolio choice problems quite generally entail 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 for our binary option structure 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 - unless success rates are positively correlated; (ii) apply to an upwardly diverse portfolio of schools. We also provide comparative statics on the chosen set.

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Paper provided by Department of Economics, W. P. Carey School of Business, Arizona State University in its series Working Papers with number 2168591.

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Handle: RePEc:asu:wpaper:2168591

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  1. 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. [Downloadable!] (restricted)
  2. James Albrecht & Pieter A. Gautier & Susan Vroman, 2006. "Equilibrium Directed Search with Multiple Applications," Review of Economic Studies, Blackwell Publishing, vol. 73(4), pages 869-891, October. [Downloadable!] (restricted)
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  3. Weitzman, Martin L, 1979. "Optimal Search for the Best Alternative," Econometrica, Econometric Society, vol. 47(3), pages 641-54, May. [Downloadable!] (restricted)
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  4. Burdett, Kenneth & Judd, Kenneth L, 1983. "Equilibrium Price Dispersion," Econometrica, Econometric Society, vol. 51(4), pages 955-69, July. [Downloadable!] (restricted)
  5. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-80, January. [Downloadable!] (restricted)
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  6. Hector Chade & Lones Smith, 2005. "Simultaneous Search," NajEcon Working Paper Reviews 172782000000000033, www.najecon.org. [Downloadable!]
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  7. 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. [Downloadable!] (restricted)
  8. Gul, Faruk & Stacchetti, Ennio, 1999. "Walrasian Equilibrium with Gross Substitutes," Journal of Economic Theory, Elsevier, vol. 87(1), pages 95-124, July. [Downloadable!] (restricted)
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  1. Pieter A. Gautier & José Luis Moraga-González & Ronald P. Wolthoff, 2007. "Structural Estimation of Search Intensity: Do Non-Employed Workers Search Enough?," IZA Discussion Papers 3045, Institute for the Study of Labor (IZA). [Downloadable!]
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  2. Hector Chade & Lones Smith, 2006. "Simultaneous Search," Cowles Foundation Discussion Papers 1556, Cowles Foundation, Yale University. [Downloadable!]
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  3. Gautier, Pieter A & Wolthoff, Ronald, 2007. "Simultaneous Search with Heterogeneous Firms and Ex Post Competition," CEPR Discussion Papers 6169, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
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  4. Philipp Kircher, 2008. "Efficiency of Simultaneous Search," PIER Working Paper Archive 08-004, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania. [Downloadable!]
  5. Manolis Galenianos & Philipp A. Kircher, 2005. "Directed Search with Multiple Job Applications," Bonn Econ Discussion Papers bgse20_2005, University of Bonn, Germany. [Downloadable!]
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