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Payoffs in exact TU economies

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  • Edhan, Omer

Abstract

We prove that a single-valued solution of perfectly competitive TU economies underlying nonatomic exact market games is uniquely determined as the Mertens [23] value by four plausible value-related axioms. Since the Mertens value is always a core element, this result provides an axiomatization of the Mertens value as a core-selection. Previous works in this direction assumed the economies to be either differentiable (e.g., Dubey and Neyman [11]) or of uniform finite-type (e.g., Haimanko [16]). Our work does not assume that, thus it contributes to the axiomatic study of payoffs in perfectly competitive economies (or values of their derived market games) in general. In fact, this is the first contribution in this direction.

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  • Edhan, Omer, 2015. "Payoffs in exact TU economies," Journal of Economic Theory, Elsevier, vol. 155(C), pages 152-184.
    • Handle: RePEc:eee:jetheo:v:155:y:2015:i:c:p:152-184
    DOI: 10.1016/j.jet.2014.11.012
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    1. Hart, Sergiu & Neyman, Abraham, 1988. "Values of non-atomic vector measure games : Are they linear combinations of the measures?," Journal of Mathematical Economics, Elsevier, vol. 17(1), pages 31-40, February.
    2. Kannai, Yakar, 1970. "Continuity Properties of the Core of a Market," Econometrica, Econometric Society, vol. 38(6), pages 791-815, November.
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    4. Mertens, J F, 1988. "The Shapley Value in the Non Differentiable Case," International Journal of Game Theory, Springer;Game Theory Society, vol. 17(1), pages 1-65.
    5. Hart, Sergiu, 1977. "Values of non-differentiable markets with a continuum of traders," Journal of Mathematical Economics, Elsevier, vol. 4(2), pages 103-116, August.
    6. Dubey, Pradeep & Neyman, Abraham, 1997. "An Equivalence Principle for Perfectly Competitive Economies," Journal of Economic Theory, Elsevier, vol. 75(2), pages 314-344, August.
    7. Haimanko, Ori, 2002. "Payoffs in Nondifferentiable Perfectly Competitive TU Economies," Journal of Economic Theory, Elsevier, vol. 106(1), pages 17-39, September.
    8. Omer Edhan, 2012. "Representations Of Positive Projections On Lipschitz Vector," Discussion Paper Series dp624, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    9. Dubey, Pradeep & Neyman, Abraham, 1984. "Payoffs in Nonatomic Economies: An Axiomatic Approach," Econometrica, Econometric Society, vol. 52(5), pages 1129-1150, September.
    10. Brown, Donald J & Robinson, Abraham, 1975. "Nonstandard Exchange Economies," Econometrica, Econometric Society, vol. 43(1), pages 41-56, January.
    11. Mertens, J.-F., 1987. "Non differentiable T.U. markets. The value," LIDAM Discussion Papers CORE 1987035, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    12. Hart, Sergiu, 1977. "Asymptotic value of games with a continuum of players," Journal of Mathematical Economics, Elsevier, vol. 4(1), pages 57-80, March.
    13. M. Amarante & F. Maccheroni & M. Marinacci & L. Montrucchio, 2006. "Cores of non-atomic market games," International Journal of Game Theory, Springer;Game Theory Society, vol. 34(3), pages 399-424, October.
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    15. Edgeworth, Francis Ysidro, 1881. "Mathematical Psychics," History of Economic Thought Books, McMaster University Archive for the History of Economic Thought, number edgeworth1881.
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    1. Omer Edhan, 2016. "Values of vector measure market games and their representations," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(1), pages 411-433, March.

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    More about this item

    Keywords

    Perfect competition; Value theory; Large economies;
    All these keywords.

    JEL classification:

    • D41 - Microeconomics - - Market Structure, Pricing, and Design - - - Perfect Competition
    • D46 - Microeconomics - - Market Structure, Pricing, and Design - - - Value Theory
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies

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