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Supermodular value functions and supermodular correspondences

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  • Pawel Dziewulski
  • John Quah

Abstract

Abstract Economic problems often involve an objective function whose value depends partly on exogenous variables and partly on actions which are chosen by an agent. We are interested in the conditions under which the resulting value is a supermodular function of the exogenous variables (after actions have been optimally chosen). Problems of this sort arise in multi-output production, optimization with non-EU models, and dynamic programming. We show that these problems can be effectively tackled through a theory of supermodular correspondences. Our work builds on early results in monotone comparative statics in Topkis (1978), Hopenhayn and Prescott (1992), and Milgrom and Shannon (1994). Revised July 2017.

Suggested Citation

  • Pawel Dziewulski & John Quah, 2016. "Supermodular value functions and supermodular correspondences," Economics Series Working Papers 795, University of Oxford, Department of Economics.
  • Handle: RePEc:oxf:wpaper:795
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    File URL: http://www.economics.ox.ac.uk/materials/papers/14485/795-dziewulski.pdf
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    References listed on IDEAS

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    1. John K.-H Quah, 2007. "The Comparative Statics of Constrained Optimization Problems," Econometrica, Econometric Society, vol. 75(2), pages 401-431, March.
    2. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-180, January.
    3. Rabah Amir, 2002. "Complementarity and Diagonal Dominance in Discounted Stochastic Games," Annals of Operations Research, Springer, vol. 114(1), pages 39-56, August.
    4. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    5. 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.
    6. 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.
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    More about this item

    Keywords

    monotone comparative statics; single crossing differences; multi-output production; ambiguity aversion; variational preferences; relative entropy; dynamic programming;

    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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