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Ratio Orderings and Comparative Statics

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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.

Suggested Citation

  • Ed Hopkins & Tatiana Kornienko, 2003. "Ratio Orderings and Comparative Statics," ESE Discussion Papers 91, Edinburgh School of Economics, University of Edinburgh.
  • Handle: RePEc:edn:esedps:91
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    References listed on IDEAS

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    1. 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 113-122, September.
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    3. Klemperer, Paul, 1999. " Auction Theory: A Guide to the Literature," Journal of Economic Surveys, Wiley Blackwell, vol. 13(3), pages 227-286, July.
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    5. Milgrom, Paul R & Weber, Robert J, 1982. "A Theory of Auctions and Competitive Bidding," Econometrica, Econometric Society, vol. 50(5), pages 1089-1122, September.
    6. Krishna, Vijay, 2009. "Auction Theory," Elsevier Monographs, Elsevier, edition 2, number 9780123745071.
    7. Milgrom, Paul, 1989. "Auctions and Bidding: A Primer," Journal of Economic Perspectives, American Economic Association, vol. 3(3), pages 3-22, Summer.
    8. Lebrun, Bernard, 1998. "Comparative Statics in First Price Auctions," Games and Economic Behavior, Elsevier, vol. 25(1), pages 97-110, October.
    9. Susan Athey, 2002. "Monotone Comparative Statics under Uncertainty," The Quarterly Journal of Economics, Oxford University Press, vol. 117(1), pages 187-223.
    10. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
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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," American Economic Review, American Economic Association, vol. 94(4), pages 1085-1107, September.
    2. Dubey, Pradeep & Geanakoplos, John, 2010. "Grading exams: 100,99,98,... or A,B,C?," Games and Economic Behavior, Elsevier, vol. 69(1), pages 72-94, May.
    3. Anastasios Papanastasiou, 2017. "Moral Hazard and Horizontal Information," Department of Economics Working Papers 2017-10, McMaster University.
    4. Pradeep Dubey & John Geanakoplos, 2014. "Games with Money and Status: How Best to Incentivize Work," Cowles Foundation Discussion Papers 1954, Cowles Foundation for Research in Economics, Yale University.

    More about this item

    Keywords

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

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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