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Universal Theory of Equilibrium in Models with Complementarities

Author

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  • Tarun Sabarwal

    (Department of Economics, University of Kansas, Lawrence, KS 66045, USA)

Abstract

We develop a universal theory of equilibrium for models with complementarities on partially ordered sets (posets), unifying lattice-based theories used widely in economics and other disciplines and poset-based theories useful to study stochastic systems in many settings. Our theorems for extremal equilibria, structure of equilibrium set, and monotone comparative statics (MCS) of equilibrium generalize both types of theories in a unified manner. This extends to new theorems for MCS of the infimum equilibrium set, supremum equilibrium set, full equilibrium set, and isotone equilibrium set, and to a universal theory of order approximation of equilibria as well. As an application, we show new, deeper structural features of equilibrium in the canonical isotone stochastic dynamic economy with correlated shocks due to Hopenhayn and Prescott (1992).

Suggested Citation

  • Tarun Sabarwal, 2023. "Universal Theory of Equilibrium in Models with Complementarities," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202312, University of Kansas, Department of Economics, revised Nov 2023.
    • Handle: RePEc:kan:wpaper:202312
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    File URL: http://www2.ku.edu/~kuwpaper/2023Papers/202312.pdf
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    References listed on IDEAS

    as
    1. 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.
    2. Roy, Sunanda & Sabarwal, Tarun, 2012. "Characterizing stability properties in games with strategic substitutes," Games and Economic Behavior, Elsevier, vol. 75(1), pages 337-353.
    3. Federico Echenique, 2002. "Comparative Statics by Adaptive Dynamics and the Correspondence Principle," Econometrica, Econometric Society, vol. 70(2), pages 833-844, March.
    4. Balbus, Lukasz & Dziewulski, Pawel & Reffett, Kevin & Wozny, Lukasz, 2022. "Markov distributional equilibrium dynamics in games with complementarities and no aggregate risk," Theoretical Economics, Econometric Society, vol. 17(2), May.
    5. Marzena Rostek & Nathan Yoder, 2020. "Matching With Complementary Contracts," Econometrica, Econometric Society, vol. 88(5), pages 1793-1827, September.
    6. Anne-Christine Barthel & Tarun Sabarwal, 2018. "Directional monotone comparative statics," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 66(3), pages 557-591, October.
    7. Daron Acemoglu & Martin Kaae Jensen, 2015. "Robust Comparative Statics in Large Dynamic Economies," Journal of Political Economy, University of Chicago Press, vol. 123(3), pages 587-640.
    8. Feng, Yue & Sabarwal, Tarun, 2020. "Strategic complements in two stage, 2 × 2 games," Journal of Economic Theory, Elsevier, vol. 190(C).
    9. Amir, Rabah, 1996. "Sensitivity analysis of multisector optimal economic dynamics," Journal of Mathematical Economics, Elsevier, vol. 25(1), pages 123-141.
    10. 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.
    11. 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.
    12. Łukasz Balbus & Paweł Dziewulski & Kevin Reffett & Łukasz Woźny, 2019. "A qualitative theory of large games with strategic complementarities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 67(3), pages 497-523, April.
    13. Yue Feng & Tarun Sabarwal, 2020. "Dynamic strategic complements in two stage, 2x2 games," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202006, University of Kansas, Department of Economics.
    14. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-1277, November.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Complementarities; Equilibrium; Fixed Point; Poset; Monotone Comparative Statics; Stochastic System.;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General

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