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Ratio Orderings and Comparative Statics

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  • Ed Hopkins

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  • Tatiana Kornienko

Abstract

Monotone ratio orderings are refinements of first order stochastic dominance that allow monotone comparative statics results in games of incomplete information. We develop analogous refinements for second order stochastic dominance based on the monotonicity of the cumulative probability ratio and the unimodality of the likelihood and probability ratios. We go on to investigate comparative statics in first price auctions, both private and common value, of the effects of more precise information in the sense of the new orderings. We find that almost all types bid more aggressively under the new distribution than they did under the old, but the highest types may bid less. This leads to higher expected revenue in a simple common value auction, but to an ambiguous result in the private value case.

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Bibliographic Info

Paper provided by Edinburgh School of Economics, University of Edinburgh in its series ESE Discussion Papers with number 91.

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Length: 32
Date of creation: Mar 2004
Date of revision:
Handle: RePEc:edn:esedps:91

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Related research

Keywords: monotone likelihood ratio; monotone probability ratio; conditional stochastic dominance; generalized Lorenz order; comparative statics; first price auctions; common value auctions;

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  1. Paul R. Milgrom, 1979. "Good Nevs and Bad News: Representation Theorems and Applications," Discussion Papers 407R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  2. Milgrom, Paul R & Weber, Robert J, 1982. "A Theory of Auctions and Competitive Bidding," Econometrica, Econometric Society, vol. 50(5), pages 1089-1122, September.
  3. Milgrom, Paul, 1989. "Auctions and Bidding: A Primer," Journal of Economic Perspectives, American Economic Association, vol. 3(3), pages 3-22, Summer.
  4. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
  5. Paul Klemperer, 1999. "Auction Theory: A Guide to the Literature," Economics Series Working Papers 1999-W12, University of Oxford, Department of Economics.
  6. Eeckhoudt, Louis & Gollier, Christian, 1995. "Demand for Risky Assets and the Monotone Probability Ratio Order," Journal of Risk and Uncertainty, Springer, vol. 11(2), pages 113-22, September.
  7. Susan Athey, 2002. "Monotone Comparative Statics Under Uncertainty," The Quarterly Journal of Economics, MIT Press, vol. 117(1), pages 187-223, February.
  8. Peter Simmons, . "Seller Surplus in First Price Auctions," Discussion Papers 96/7, Department of Economics, University of York.
  9. Shorrocks, Anthony F, 1983. "Ranking Income Distributions," Economica, London School of Economics and Political Science, vol. 50(197), pages 3-17, February.
  10. Athey, Susan, 2002. "Monotone Comparative Statics Under Uncertainty," Scholarly Articles 3372263, Harvard University Department of Economics.
  11. Lebrun, Bernard, 1998. "Comparative Statics in First Price Auctions," Games and Economic Behavior, Elsevier, vol. 25(1), pages 97-110, October.
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Cited by:
  1. Ed Hopkins & Tatiana Kornienko, 2004. "Running to Keep in the Same Place: Consumer Choice as a Game of Status," ESE Discussion Papers 92, Edinburgh School of Economics, University of Edinburgh.
  2. Pradeep Dubey & John Geanakoplos, 2009. "Grading Exams: 100, 99, 98,...or A, B, C?," Cowles Foundation Discussion Papers 1710, Cowles Foundation for Research in Economics, Yale University.
  3. Pradeep Dubey & John Geanakoplos, 2009. "Grading Exams: 100, 99, 98,... or A, B, C?," Levine's Working Paper Archive 814577000000000361, David K. Levine.

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