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Equilibria and Indivisibilities: Gross Substitutes and Complements


  • Ning Sun
  • Zaifu Yang


This paper examines an exchange economy with heterogeneous indivisible objects that can be substitutable or complementary. We show that a competitive equilibrium exists in such economies, provided that all the objects can be partitioned into two groups, and from the viewpoint of each agent, objects in the same group are substitutes and objects across the two groups are complements. This condition generalizes the well-known Kelso-Crawford gross substitutes condition and is called gross substitutes and complements. We also provide practical and typical examples from which substitutes and complements are both jointly observed. Copyright The Econometric Society 2006.

Suggested Citation

  • Ning Sun & Zaifu Yang, 2006. "Equilibria and Indivisibilities: Gross Substitutes and Complements," Econometrica, Econometric Society, vol. 74(5), pages 1385-1402, September.
  • Handle: RePEc:ecm:emetrp:v:74:y:2006:i:5:p:1385-1402

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    References listed on IDEAS

    1. Nabil I. Al-Najjar & Jonathan Weinstein, 2008. "Comparative Testing of Experts," Econometrica, Econometric Society, vol. 76(3), pages 541-559, May.
    2. Lovell, Michael C, 1986. "Tests of the Rational Expectations Hypothesis," American Economic Review, American Economic Association, vol. 76(1), pages 110-124, March.
    3. LeRoy, Stephen F & Singell, Larry D, Jr, 1987. "Knight on Risk and Uncertainty," Journal of Political Economy, University of Chicago Press, vol. 95(2), pages 394-406, April.
    4. Ottaviani, Marco & Sorensen, Peter Norman, 2006. "The strategy of professional forecasting," Journal of Financial Economics, Elsevier, vol. 81(2), pages 441-466, August.
    5. Fudenberg, Drew & Levine, David K., 1999. "An Easier Way to Calibrate," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 131-137, October.
    6. Trueman, Brett, 1988. " A Theory of Noise Trading in Securities Markets," Journal of Finance, American Finance Association, vol. 43(1), pages 83-95, March.
    7. Morgan, John & Stocken, Phillip C, 2003. " An Analysis of Stock Recommendations," RAND Journal of Economics, The RAND Corporation, vol. 34(1), pages 183-203, Spring.
    8. Michael P. Keane & David E. Runkle, 1998. "Are Financial Analysts' Forecasts of Corporate Profits Rational?," Journal of Political Economy, University of Chicago Press, vol. 106(4), pages 768-805, August.
    9. Alvaro Sandroni, 2003. "The reproducible properties of correct forecasts," International Journal of Game Theory, Springer;Game Theory Society, vol. 32(1), pages 151-159, December.
    10. Eddie Dekel & Yossi Feinberg, 2006. "Non-Bayesian Testing of a Stochastic Prediction," Review of Economic Studies, Oxford University Press, vol. 73(4), pages 893-906.
    11. Wojciech Olszewski & Alvaro Sandroni, 2006. "Strategic Manipulation of Empirical Tests," Discussion Papers 1425, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    12. P. Frevert, 1971. "Note," Review of Economic Studies, Oxford University Press, vol. 38(2), pages 269-270.
    13. Vladimir Vovk & Glenn Shafer, 2005. "Good randomized sequential probability forecasting is always possible," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 747-763.
    14. Keane, Michael P & Runkle, David E, 1990. "Testing the Rationality of Price Forecasts: New Evidence from Panel Data," American Economic Review, American Economic Association, vol. 80(4), pages 714-735, September.
    15. David Laster & Paul Bennett & In Sun Geoum, 1999. "Rational Bias in Macroeconomic Forecasts," The Quarterly Journal of Economics, Oxford University Press, vol. 114(1), pages 293-318.
    16. Alvaro Sandroni & Wojciech Olszewski, 2008. "Falsifiability," PIER Working Paper Archive 08-016, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    17. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    18. Sandroni, Alvaro & Olszewski, Wojciech, 2007. "Contracts and uncertainty," Theoretical Economics, Econometric Society, vol. 2(1), pages 1-13, March.
    19. Shmaya, Eran, 2008. "Many inspections are manipulable," Theoretical Economics, Econometric Society, vol. 3(3), September.
    20. Yossi Feinberg & Colin Stewart, 2008. "Testing Multiple Forecasters," Econometrica, Econometric Society, vol. 76(3), pages 561-582, May.
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