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Comparative Statics, Informativeness, and the Interval Dominance Order

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  • John K.-H. Quah

    ()
    (Department of Economics, Oxford University)

  • Bruno Strulovici

    ()
    (Department of Economics, Oxford University)

Abstract

We identify a natural way of ordering functions, which we call the interval dominance order and develop a theory of monotone comparative statics based on this order. This way of ordering functions is weaker then the standard one based on the single crossing property (Milgrom and Shannon, 1994) and so our results apply in some settings where the single crossing property does not hold. For example, they are useful when examining the comparative statics of optimal stopping time problems. We also show that certain basic results in statistical decision theory which are important in economics – specifically, the complete class theorem of Karlin and Rubin (1956) and the results connected with Lehmann’s (1988) concept of informativeness – generalize to payoff functions obeying the interval dominance order.

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File URL: http://www.nuffield.ox.ac.uk/economics/papers/2007/w4/hlp27.pdf
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Bibliographic Info

Paper provided by Economics Group, Nuffield College, University of Oxford in its series Economics Papers with number 2007-W04.

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Length: 40 pages
Date of creation: 03 Sep 2007
Date of revision:
Handle: RePEc:nuf:econwp:0704

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Web page: http://www.nuff.ox.ac.uk/economics/

Related research

Keywords: single crossing property; interval dominance order; supermodularity; comparative statics; optimal stopping time; complete class theorem; statistical decision theory; informativeness;

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References

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  1. Jonathan Levin & Susan Athey, 2001. "The Value of Information in Monotone Decision Problems," Working Papers, Stanford University, Department of Economics 01003, Stanford University, Department of Economics.
  2. Ormiston Michael B. & Schlee Edward E., 1993. "Comparative Statics under Uncertainty for a Class of Economic Agents," Journal of Economic Theory, Elsevier, Elsevier, vol. 61(2), pages 412-422, December.
  3. Athey, Susan, 2002. "Monotone Comparative Statics Under Uncertainty," Scholarly Articles 3372263, Harvard University Department of Economics.
  4. Milgrom, P. & Shannon, C., 1991. "Monotone Comparative Statics," Papers, Stanford - Institute for Thoretical Economics 11, Stanford - Institute for Thoretical Economics.
  5. Susan Athey, 2002. "Monotone Comparative Statics Under Uncertainty," The Quarterly Journal of Economics, MIT Press, MIT Press, vol. 117(1), pages 187-223, February.
  6. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, Econometric Society, vol. 58(6), pages 1255-77, November.
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Citations

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Cited by:
  1. Roy, Sunanda & Sabarwal, Tarun, 2012. "Characterizing Stability Properties in Games with Strategic Substitutes," Staff General Research Papers, Iowa State University, Department of Economics 34778, Iowa State University, Department of Economics.
  2. Darrell Duffie & Bruno Strulovici, 2009. "Capital Mobility and Asset Pricing," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 1478, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  3. John Quah & Bruno Strulovici, 2011. "Discounting, Patience, and Dynamic Decision Making," Economics Series Working Papers, University of Oxford, Department of Economics 555, University of Oxford, Department of Economics.
  4. Andrew Monaco & Tarun Sabarwal, 2012. "Games with Strategic Heterogeneity," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS, University of Kansas, Department of Economics 201240, University of Kansas, Department of Economics, revised Nov 2012.
  5. Strulovici, Bruno & Szydlowski, Martin, 2012. "On the Smoothness of Value Functions," MPRA Paper 36326, University Library of Munich, Germany, revised 31 Jan 2012.
  6. Natalia Lazzati, 2013. "Comparison of equilibrium actions and payoffs across players in games of strategic complements," Economic Theory, Springer, Springer, vol. 54(3), pages 777-788, November.
  7. Luciano De Castro, 2012. "Correlation of Types in Bayesian Games," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 1556, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  8. Andrew Monaco & Tarun Sabarwal, 2012. "Monotone Comparative Statics in Games with both Strategic Complements and Strategic Substitutes," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS, University of Kansas, Department of Economics 201236, University of Kansas, Department of Economics, revised Aug 2012.
  9. John K. -H Quah & Bruno Strulovici, 2009. "Discounting and Patience in Optimal Stopping and Control Problems," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 1480, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  10. Kukushkin, Nikolai S., 2013. "Approximate Nash equilibrium under the single crossing conditions," MPRA Paper 44320, University Library of Munich, Germany.
  11. Roger Guesnerie & Pedro Jara-Moroni, 2011. "Expectational coordination in simple economic contexts," Economic Theory, Springer, Springer, vol. 47(2), pages 205-246, June.

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