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A revealed preference theory of monotone choice and strategic complementarity

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  • John K.-H. Quah

    () (Department of Economics, University of Oxford)

  • Koji Shirai

    (Institute of Economic Research, Kyoto University)

Abstract

We carry out a revealed preference analysis of monotone comparative statics. We ask what restrictions on an agent's observed choice behavior are necessary and sufficient to rationalize the data with a preference guaranteeing that choices are always monotone with re- spect to a parameter. We extend our analysis to a game-theoretic setting where players' chosen actions, the strategy sets from which actions are chosen, and the parameters which may affect payoffs are observed. Variation in the data arises from changes to parameters and/or changes to the strategy sets. We show that an intuitive and easy-to-check property on the data set is necessary and sufficient for it to be consistent with the hypothesis that each observation is a pure strategy Nash equilibrium in a game with strategic complementarity. When a data set obeys this property, we show how to exploit this data to identify the set of possible Nash equilibria in a game outside the set of observations.

Suggested Citation

  • John K.-H. Quah & Koji Shirai, 2015. "A revealed preference theory of monotone choice and strategic complementarity," KIER Working Papers 914, Kyoto University, Institute of Economic Research.
    • Handle: RePEc:kyo:wpaper:914
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    References listed on IDEAS

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    3. Yuichi Kitamura & Jörg Stoye, 2018. "Nonparametric Analysis of Random Utility Models," Econometrica, Econometric Society, vol. 86(6), pages 1883-1909, November.
    4. Kukushkin, Nikolai S. & Quah, John K.-H. & Shirai, Koji, 2016. "A counterexample on the completion of preferences with single crossing differences," MPRA Paper 73760, University Library of Munich, Germany.
    5. John K.-H. Quah & Bruno Strulovici, 2009. "Comparative Statics, Informativeness, and the Interval Dominance Order," Econometrica, Econometric Society, vol. 77(6), pages 1949-1992, November.
    6. Zhou Lin, 1994. "The Set of Nash Equilibria of a Supermodular Game Is a Complete Lattice," Games and Economic Behavior, Elsevier, vol. 7(2), pages 295-300, September.
    7. Stoye, Jörg & Kitamura, Yuichi, 2013. "Nonparametric Analysis of Random Utility Models: Testing," Annual Conference 2013 (Duesseldorf): Competition Policy and Regulation in a Global Economic Order 79753, Verein für Socialpolitik / German Economic Association.
    8. Milgrom, Paul & Roberts, John, 1994. "Comparing Equilibria," American Economic Review, American Economic Association, vol. 84(3), pages 441-459, June.
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    Cited by:

    1. Kukushkin, Nikolai S. & Quah, John K.-H. & Shirai, Koji, 2016. "A counterexample on the completion of preferences with single crossing differences," MPRA Paper 73760, University Library of Munich, Germany.
    2. Yuichi Kitamura & Jörg Stoye, 2018. "Nonparametric Analysis of Random Utility Models," Econometrica, Econometric Society, vol. 86(6), pages 1883-1909, November.
    3. Sobel, Joel, 2019. "Iterated weak dominance and interval-dominance supermodular games," Theoretical Economics, Econometric Society, vol. 14(1), January.

    More about this item

    Keywords

    monotone comparative statics; single crossing di erences; interval dominance; supermodular games; lattices;

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D7 - Microeconomics - - Analysis of Collective Decision-Making

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