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General theory of equilibrium in models with complementarities

Author

Listed:
  • Tarun Sabarwal

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

Abstract
We unify and generalize the equilibrium theory of foundational models of complementarities used widely in economics and other disciplines. Widely used results for existence of extremal equilibrium, nonempty complete lattice structure of the equilibrium set, and monotone comparative statics (MCS) of extremal equilibria are unified and generalized, subsuming the results for standard and neostandard models as special cases and allowing for new situations. Structure theorems due to Tarski (1955) and Zhou (1994) are generalized without using the strong set order or subcompleteness. Defining new set orders, we formulate new theories for structural comparisons of equilibrium sets, and prove new theorems for MCS of the infimum equilibrium set, the supremum equilibrium set, and the full equilibrium set. Order comparability of equilibrium sets provides a new theory of order approximation of equilibria as well. Our off-the-shelf theorems apply regardless of the manner in which individual choices are made as long as they satisfy our weak conditions, which are proved to hold in standard and neostandard models.

Suggested Citation

  • Tarun Sabarwal, 2023. "General theory of equilibrium in models with complementarities," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202307, University of Kansas, Department of Economics, revised Sep 2023.
    • Handle: RePEc:kan:wpaper:202307
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    File URL: http://www2.ku.edu/~kuwpaper/2023Papers/202307.pdf
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    References listed on IDEAS

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    14. Anne-Christine Barthel & Eric Hoffmann & Tarun Sabarwal, 2021. "A Unified Approach to p-Dominance and its Generalizations in Games with Strategic Complements and Substitutes," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202109, University of Kansas, Department of Economics.
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    Cited by:

    1. Lu Yu, 2024. "Generalization of Zhou fixed point theorem," Papers 2407.17884, arXiv.org.
    2. Lu Yu, 2024. "Order-theoretical fixed point theorems for correspondences and application in game theory," Papers 2407.18582, arXiv.org.

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    More about this item

    Keywords

    Complementarities; Equilibrium; Fixed point; Strategic complements; Monotone comparative statics;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General

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