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Bargaining set and anonymous core without the monotonicity assumption

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  • Hara, Chiaki

Abstract

We give an example of an atomless exchange economy in which consumers'preference relations are not monotone and in which the bargaining set of Mas-Colell (1989) consists of all allocations satisfying resource constraints, although the set of all Walrasian equilibrium allocations, the core, and the anonymous core of Hara (2002) are all empty. We also give an equivalence theorem for the anonymous core when the preference relations may not be monotone.
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  • Hara, Chiaki, 2005. "Bargaining set and anonymous core without the monotonicity assumption," Journal of Mathematical Economics, Elsevier, vol. 41(4-5), pages 545-556, August.
    • Handle: RePEc:eee:mateco:v:41:y:2005:i:4-5:p:545-556
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    1. Robert M. Anderson & Walter Trockel & Lin Zhou, 1997. "Nonconvergence of the Mas-Colell and Zhou Bargaining Sets," Econometrica, Econometric Society, vol. 65(5), pages 1227-1240, September.
    2. Schmeidler, David, 1969. "Competitive Equilibria in Markets with a Continuum of Traders and Incomplete Preferences," Econometrica, Econometric Society, vol. 37(4), pages 578-585, October.
    3. Hildenbrand, Werner, 1970. "Existence of Equilibria for Economies with Production and a Measure Space of Consumers," Econometrica, Econometric Society, vol. 38(5), pages 608-623, September.
    4. Mas-Colell, Andreu, 1989. "An equivalence theorem for a bargaining set," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 129-139, April.
    5. Peter J. Hammond, 1979. "Straightforward Individual Incentive Compatibility in Large Economies," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 46(2), pages 263-282.
    6. Gerard Debreu, 1956. "Market Equilibrium," Cowles Foundation Discussion Papers 10, Cowles Foundation for Research in Economics, Yale University.
    7. Husseinov, Farhad, 1999. "Boundary Behavior of Excess Demand and Existence of Equilibrium," Journal of Economic Theory, Elsevier, vol. 87(2), pages 434-449, August.
    8. Manelli, Alejandro M, 1991. "Monotonic Preferences and Core Equivalence," Econometrica, Econometric Society, vol. 59(1), pages 123-138, January.
    9. Gerard Debreu, 1963. "On a Theorem of Scarf," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 30(3), pages 177-180.
    10. Chiaki Hara, 2005. "Existence of Equilibria in Economies with Bads," Econometrica, Econometric Society, vol. 73(2), pages 647-658, March.
    11. Hara, Chiaki, 2002. "The anonymous core of an exchange economy," Journal of Mathematical Economics, Elsevier, vol. 38(1-2), pages 91-116, September.
    12. Neuefeind, Wilhelm, 1980. "Notes on Existence of Equilibrium Proofs and the Boundary Behavior of Supply," Econometrica, Econometric Society, vol. 48(7), pages 1831-1837, November.
    13. Manelli, Alejandro M., 1991. "Core convergence without monotone preferences and free disposal," Journal of Economic Theory, Elsevier, vol. 55(2), pages 400-415, December.
    14. Broome, John, 1972. "Approximate equilibrium in economies with indivisible commodities," Journal of Economic Theory, Elsevier, vol. 5(2), pages 224-249, October.
    15. HILDENBRAND, Werner, 1970. "Existence of equilibria for economies with production and a measure space of consumers," LIDAM Reprints CORE 79, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Cited by:

    1. Elena Iñarra & Roberto Serrano & Ken-Ichi Shimomura, 2020. "The Nucleolus, the Kernel, and the Bargaining Set: An Update," Revue économique, Presses de Sciences-Po, vol. 71(2), pages 225-266.
    2. Yang, Yi-You, 2015. "On the Maximal Domain Theorem," MPRA Paper 67265, University Library of Munich, Germany.

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    More about this item

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D41 - Microeconomics - - Market Structure, Pricing, and Design - - - Perfect Competition
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • Q53 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - Air Pollution; Water Pollution; Noise; Hazardous Waste; Solid Waste; Recycling

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