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Supermodular correspondences and comparison of multi-prior beliefs

Author

Listed:
  • Pawel Dziewulski

    (Department of Economics, University of Sussex, Brighton, UK)

  • John K. H. Quah

    (Department of Economics, John Hopkins University and Department of Economics, National University of Singapore)

Abstract

Economic decisions often involve maximising an objective whose value is itself the outcome of another optimisation problem. This decision structure arises in multi-output production and choice under uncertainty with multi-prior beliefs. To analyse comparative statics in these models, we introduce a theory of Supermodular correspondences. In particular, we employ this theory to generalise the notion of first order stochastic dominance to multi-prior beliefs, allowing us to characterise conditions under which greater optimism leads to higher action.

Suggested Citation

  • Pawel Dziewulski & John K. H. Quah, 2019. "Supermodular correspondences and comparison of multi-prior beliefs," Working Paper Series 0619, Department of Economics, University of Sussex Business School.
    • Handle: RePEc:sus:susewp:0619
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    References listed on IDEAS

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    1. Mark Huggett, 2003. "When Are Comparative Dynamics Monotone?," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 6(1), pages 1-11, January.
    2. , & ,, 2014. "Stochastic stability in monotone economies," Theoretical Economics, Econometric Society, vol. 9(2), May.
    3. Tomasz Strzalecki, 2011. "Axiomatic Foundations of Multiplier Preferences," Econometrica, Econometric Society, vol. 79(1), pages 47-73, January.
    4. Lars Peter Hansen & Thomas J Sargent, 2014. "Robust Control and Model Uncertainty," World Scientific Book Chapters, in: UNCERTAINTY WITHIN ECONOMIC MODELS, chapter 5, pages 145-154, World Scientific Publishing Co. Pte. Ltd..
    5. John K.-H Quah, 2007. "The Comparative Statics of Constrained Optimization Problems," Econometrica, Econometric Society, vol. 75(2), pages 401-431, March.
    6. Christian Gollier, 2011. "Portfolio Choices and Asset Prices: The Comparative Statics of Ambiguity Aversion," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 78(4), pages 1329-1344.
    7. Epstein, Larry G. & Schneider, Martin, 2003. "Recursive multiple-priors," Journal of Economic Theory, Elsevier, vol. 113(1), pages 1-31, November.
    8. Balbus, Łukasz & Reffett, Kevin & Woźny, Łukasz, 2014. "A constructive study of Markov equilibria in stochastic games with strategic complementarities," Journal of Economic Theory, Elsevier, vol. 150(C), pages 815-840.
    9. Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo, 2004. "Differentiating ambiguity and ambiguity attitude," Journal of Economic Theory, Elsevier, vol. 118(2), pages 133-173, October.
    10. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    11. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-180, January.
    12. Hopenhayn, Hugo A & Prescott, Edward C, 1992. "Stochastic Monotonicity and Stationary Distributions for Dynamic Economies," Econometrica, Econometric Society, vol. 60(6), pages 1387-1406, November.
    13. Cherbonnier, Frédéric & Gollier, Christian, 2015. "Decreasing aversion under ambiguity," Journal of Economic Theory, Elsevier, vol. 157(C), pages 606-623.
    14. Milgrom, Paul & Roberts, John, 1990. "The Economics of Modern Manufacturing: Technology, Strategy, and Organization," American Economic Review, American Economic Association, vol. 80(3), pages 511-528, June.
    15. Curtat, Laurent O., 1996. "Markov Equilibria of Stochastic Games with Complementarities," Games and Economic Behavior, Elsevier, vol. 17(2), pages 177-199, December.
    16. Garud N. Iyengar, 2005. "Robust Dynamic Programming," Mathematics of Operations Research, INFORMS, vol. 30(2), pages 257-280, May.
    17. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, June.
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    Cited by:

    1. Bar Light, 2021. "Stochastic Comparative Statics in Markov Decision Processes," Mathematics of Operations Research, INFORMS, vol. 46(2), pages 797-810, May.
    2. Bar Light, 2019. "Stochastic Comparative Statics in Markov Decision Processes," Papers 1904.05481, arXiv.org, revised Jan 2020.

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    More about this item

    Keywords

    monotone comparative statics; supermodularity; correspondences; stochastic dominance; multi-output production; ambiguity; dynamic programming;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D21 - Microeconomics - - Production and Organizations - - - Firm Behavior: Theory
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity

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