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Strategic Complementarities and Search Market Equilibrium

  • Michael T. Rauh

    (Department of Business Economics and Public Policy, Indiana University Kelley School of Business)

In this paper, we apply supermodular game theory to the equilibrium search literature with sequential search. We identify necessary and sufficient conditions for strategic complementarities and prove existence of search market equilibrium. When firms are identical, the Diamond Paradox obtains and is robust within the class of search cost densities that are small near zero and support strategic complementarities. Price dispersion is therefore inherently incompatible with strategic complementarities. Finally, we show that a major criticism of the literature, that agents act as if they know the distribution of prices, can be justified in the sense of convergent best response dynamics.

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File URL: http://kelley.iu.edu/riharbau/RePEc/iuk/wpaper/bepp2006-01-rauh.pdf
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Paper provided by Indiana University, Kelley School of Business, Department of Business Economics and Public Policy in its series Working Papers with number 2006-01.

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Date of creation: 2006
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Handle: RePEc:iuk:wpaper:2006-01
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  1. Maarten C. W. Janssen & José Luis Moraga-González, 2004. "Strategic Pricing, Consumer Search and the Number of Firms," Review of Economic Studies, Wiley Blackwell, vol. 71(4), pages 1089-1118, October.
  2. Burdett, Kenneth & Judd, Kenneth L, 1983. "Equilibrium Price Dispersion," Econometrica, Econometric Society, vol. 51(4), pages 955-69, July.
  3. Stahl, Dale O, II, 1989. "Oligopolistic Pricing with Sequential Consumer Search," American Economic Review, American Economic Association, vol. 79(4), pages 700-712, September.
  4. Ed Hopkins & Robert M Seymour, 2004. "The Stability of Price Dispersion under Seller and Consumer Learning," ESE Discussion Papers 52, Edinburgh School of Economics, University of Edinburgh.
  5. Rauh, Michael T., 2007. "Nonstandard foundations of equilibrium search models," Journal of Economic Theory, Elsevier, vol. 132(1), pages 518-529, January.
  6. Michael Rothschild, 1974. "Searching for the Lowest Price When the Distribution of Prices Is Unknown: A Summary," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 3, number 1, pages 293-294 National Bureau of Economic Research, Inc.
  7. Matthijs R. Wildenbeest, 2011. "An empirical model of search with vertically differentiated products," RAND Journal of Economics, RAND Corporation, vol. 42(4), pages 729-757, December.
  8. Michael T. Rauh, 2003. "Non-cooperative games with a continuum of players whose payoffs depend on summary statistics," Economic Theory, Springer, vol. 21(4), pages 901-906, 06.
  9. Benabou, Roland & Gertner, Robert, 1993. "Search with Learning from Prices: Does Increased Inflationary Uncertainty Lead to Higher Markups?," Review of Economic Studies, Wiley Blackwell, vol. 60(1), pages 69-94, January.
  10. Echenique, Federico & Edlin, Aaron S., 2004. "Mixed equilibria are unstable in games of strategic complements," Berkeley Olin Program in Law & Economics, Working Paper Series qt1ht651hk, Berkeley Olin Program in Law & Economics.
  11. Carlson, John A & McAfee, R Preston, 1983. "Discrete Equilibrium Price Dispersion," Journal of Political Economy, University of Chicago Press, vol. 91(3), pages 480-93, June.
  12. Rauh, Michael T., 1997. "A Model of Temporary Search Market Equilibrium," Journal of Economic Theory, Elsevier, vol. 77(1), pages 128-153, November.
  13. Benabou Roland, 1993. "Search Market Equilibrium, Bilateral Heterogeneity, and Repeat Purchases," Journal of Economic Theory, Elsevier, vol. 60(1), pages 140-158, June.
  14. Rothschild, Michael, 1974. "Searching for the Lowest Price When the Distribution of Prices Is Unknown," Journal of Political Economy, University of Chicago Press, vol. 82(4), pages 689-711, July/Aug..
  15. Moraga-González, José Luis & Wildenbeest, Matthijs R., 2008. "Maximum likelihood estimation of search costs," European Economic Review, Elsevier, vol. 52(5), pages 820-848, July.
  16. Dana, J.D., 1991. "Learning in an Equilibrium Search Model," Papers 37, Stanford - Institute for Thoretical Economics.
  17. Michael R. Baye & John Morgan & Patrick Scholten, 2006. "Information, Search, and Price Dispersion," Working Papers 2006-11, Indiana University, Kelley School of Business, Department of Business Economics and Public Policy.
  18. Rob, Rafael, 1985. "Equilibrium Price Distributions," Review of Economic Studies, Wiley Blackwell, vol. 52(3), pages 487-504, July.
  19. Khan, M. Ali & Sun, Yeneng, 1999. "Non-cooperative games on hyperfinite Loeb spaces1," Journal of Mathematical Economics, Elsevier, vol. 31(4), pages 455-492, May.
  20. Michael R. Baye & John Morgan, 2001. "Information Gatekeepers on the Internet and the Competitiveness of Homogeneous Product Markets," American Economic Review, American Economic Association, vol. 91(3), pages 454-474, June.
  21. Jennifer F. Reinganum, 1978. "A Simple Model of Equilibrium Price Dispersion," Discussion Papers 335, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  22. Stahl, Dale O., 1996. "Oligopolistic pricing with heterogeneous consumer search," International Journal of Industrial Organization, Elsevier, vol. 14(2), pages 243-268.
  23. Haomiao Yu & Wei Zhu, 2005. "Large games with transformed summary statistics," Economic Theory, Springer, vol. 26(1), pages 237-241, 07.
  24. Han Hong & Matthew Shum, 2006. "Using price distributions to estimate search costs," RAND Journal of Economics, RAND Corporation, vol. 37(2), pages 257-275, 06.
  25. Babur de los Santos, 2008. "Consumer Search on the Internet," Working Papers 2008-06, Indiana University, Kelley School of Business, Department of Business Economics and Public Policy.
  26. repec:dgr:uvatin:20070102 is not listed on IDEAS
  27. Diamond, Peter A., 1971. "A model of price adjustment," Journal of Economic Theory, Elsevier, vol. 3(2), pages 156-168, June.
  28. Varian, Hal R, 1980. "A Model of Sales," American Economic Review, American Economic Association, vol. 70(4), pages 651-59, September.
  29. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-77, November.
  30. Janssen, Maarten C.W. & Moraga-Gonzalez, Jose Luis & Wildenbeest, Matthijs R., 2005. "Truly costly sequential search and oligopolistic pricing," International Journal of Industrial Organization, Elsevier, vol. 23(5-6), pages 451-466, June.
  31. Vives, X., 1988. "Nash Equilibrium With Strategic Complementarities," UFAE and IAE Working Papers 107-88, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  32. Rauh, Michael T., 2004. "Wage and price controls in the equilibrium sequential search model," European Economic Review, Elsevier, vol. 48(6), pages 1287-1300, December.
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