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Back to Fundamentals: Equilibrium in Abstract Economies

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  • Richter, Michael
  • Rubinstein, Ariel

Abstract

We propose a new abstract definition of equilibrium in the spirit of competitive equilibrium: a profile of alternatives and a public ordering (expressing prestige, price or a social norm), such that each agent prefers his assigned alternative to all lower-ranked ones. The equilibrium operates in an abstract setting built upon a concept of convexity borrowed from Convex Geometry. We apply the concept to a variety of convex economies and relate it to Pareto optimality. The "magic" of linear equilibrium prices is put into perspective by establishing an analogy between linear functions in the standard convexity and "primitive orderings" in the abstract convexity.

Suggested Citation

  • Richter, Michael & Rubinstein, Ariel, 2015. "Back to Fundamentals: Equilibrium in Abstract Economies," Foerder Institute for Economic Research Working Papers 275833, Tel-Aviv University > Foerder Institute for Economic Research.
    • Handle: RePEc:ags:isfiwp:275833
    DOI: 10.22004/ag.econ.275833
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    References listed on IDEAS

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    1. Michele Piccione & Ariel Rubinstein, 2007. "Equilibrium in the Jungle," Economic Journal, Royal Economic Society, vol. 117(522), pages 883-896, July.
    2. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
    3. Koshevoy, Gleb A., 1999. "Choice functions and abstract convex geometries," Mathematical Social Sciences, Elsevier, vol. 38(1), pages 35-44, July.
    4. Jens Gudmundsson, 2014. "When do stable roommate matchings exist? A review," Review of Economic Design, Springer;Society for Economic Design, vol. 18(2), pages 151-161, June.
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    Cited by:

    1. Herings, P. Jean-Jacques, 2024. "Expectational equilibria in many-to-one matching models with contracts," Journal of Economic Theory, Elsevier, vol. 216(C).
    2. Olkhov, Victor, 2018. "Economic Transactions Govern Business Cycles," MPRA Paper 88531, University Library of Munich, Germany, revised 19 Aug 2018.
    3. Chambers, Christopher P. & Miller, Alan D. & Yenmez, M. Bumin, 2020. "Closure and preferences," Journal of Mathematical Economics, Elsevier, vol. 88(C), pages 161-166.
    4. Herings, P. Jean-Jacques, 2020. "Expectational Equilibria in Many-to-one Matching Models with Contracts - A Reformulation of Competitive Equilibrium," Research Memorandum 018, Maastricht University, Graduate School of Business and Economics (GSBE).
    5. Tony Bryant & Doug McLeod, 2020. "The Guidance of an Enterprise Economy," The Economic Record, The Economic Society of Australia, vol. 96(313), pages 209-210, June.
    6. Ivan Balbuzanov & Maciej H. Kotowski, 2019. "Endowments, Exclusion, and Exchange," Econometrica, Econometric Society, vol. 87(5), pages 1663-1692, September.
    7. Richter, Michael & Rubinstein, Ariel, 2020. "The permissible and the forbidden," Journal of Economic Theory, Elsevier, vol. 188(C).
    8. Beißner, Patrick & Riedel, Frank, 2016. "Knight-Walras equilibria," Center for Mathematical Economics Working Papers 558, Center for Mathematical Economics, Bielefeld University.
    9. Elizabeth Baldwin & Paul Klemperer, 2019. "Understanding Preferences: “Demand Types”, and the Existence of Equilibrium With Indivisibilities," Econometrica, Econometric Society, vol. 87(3), pages 867-932, May.
    10. Hamed Hamze Bajgiran & Federico Echenique, 2022. "Closure operators: Complexity and applications to classification and decision-making," Papers 2202.05339, arXiv.org, revised May 2022.
    11. Patrick Beissner & Frank Riedel, 2019. "Equilibria Under Knightian Price Uncertainty," Econometrica, Econometric Society, vol. 87(1), pages 37-64, January.
    12. Beissner, Patrick & Werner, Jan, 2023. "Optimal allocations with α-MaxMin utilities, Choquet expected utilities, and Prospect Theory," Theoretical Economics, Econometric Society, vol. 18(3), July.
    13. M. Ali Khan & Metin Uyanık, 2021. "Topological connectedness and behavioral assumptions on preferences: a two-way relationship," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(2), pages 411-460, March.
    14. O'Callaghan, Patrick, 2016. "Measuring utility without mixing apples and oranges and eliciting beliefs about stock prices," MPRA Paper 69363, University Library of Munich, Germany.
    15. Somdeb Lahiri, 2017. "Competitive Equilibrium in Generalized Games: A New Interpretation," Studies in Microeconomics, , vol. 5(1), pages 35-52, June.
    16. Olkhov, Victor, 2018. "Economic and Financial Transactions Govern Business Cycles," MPRA Paper 93269, University Library of Munich, Germany.
    17. Victor Olkhov, 2018. "Econophysics Beyond General Equilibrium: the Business Cycle Model," Papers 1804.04721, arXiv.org.
    18. Ariel Rubinstein & Kemal Yıldız, 2022. "An étude in modeling the definability of equilibrium," Review of Economic Design, Springer;Society for Economic Design, vol. 26(4), pages 543-552, December.
    19. Richter, Michael & Rubinstein, Ariel, 2024. "Unilateral stability in matching problems," Journal of Economic Theory, Elsevier, vol. 216(C).
    20. Balbuzanov, Ivan & Kotowski, Maciej H., 0. "The property rights theory of production networks," Theoretical Economics, Econometric Society.
    21. Annie Tubadji, 2020. "Value-Free Analysis of Values: A Culture-Based Development Approach," Sustainability, MDPI, vol. 12(22), pages 1-17, November.
    22. Brendan Markey-Towler, 2016. "Law of the jungle: firm survival and price dynamics in evolutionary markets," Journal of Evolutionary Economics, Springer, vol. 26(3), pages 655-696, July.
    23. Miralles, Antonio & Pycia, Marek, 2021. "Foundations of pseudomarkets: Walrasian equilibria for discrete resources," Journal of Economic Theory, Elsevier, vol. 196(C).

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    More about this item

    Keywords

    Financial Economics; Research Methods/ Statistical Methods;

    JEL classification:

    • C90 - Mathematical and Quantitative Methods - - Design of Experiments - - - General
    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • H00 - Public Economics - - General - - - General

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