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Markets, Arbitrage and Social Choices


  • CHICHILNISKY , Graciela

    (Columbia University)


The paper establishes a clear connection between equilibrium theory and social choice theory by showing that, for a well defined social choice problem, the conditions which are necessary and sufficient to solve this problem are the same as the conditions which are necessary and sufficient to establish existence of a competitive equilibrium. We define a condition of limited arbitrage on the preferences and the endowments of an Arrow-Debreu economy. This bounds the utility gains that the traders can afford from their initial endowments. Theorem 2 proves that limited arbitrage is necessary and sufficient for the existence of a sodal choice rule which allocates society's resources among individuals in a manner which depends continuously and anonymously on their preferences over allocations, and which respects unanimity. Limited arbitrage is also necessary and sufficient for the existence of a competitive equilibrium in the Arrow - Debreu economy, with or without bounds on short sales, Theorem 7. Theorem 4 proves that any market allocation can be achieved as a social choice allocation, i.e. an allocation which is maximal among all feasible allocations according to a social preference defined via a social choice rule which is continuous, anonymous and respects unanimity.

Suggested Citation

  • CHICHILNISKY , Graciela, 1993. "Markets, Arbitrage and Social Choices," CORE Discussion Papers 1993042, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  • Handle: RePEc:cor:louvco:1993042

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    References listed on IDEAS

    1. Bacharach, Michael, 1985. "Some extensions of a claim of Aumann in an axiomatic model of knowledge," Journal of Economic Theory, Elsevier, vol. 37(1), pages 167-190, October.
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    5. LISMONT, Luc & MONGIN, Philippe, 1994. "On the Logic of Common Belief and Common Knowledge," CORE Discussion Papers 1994005, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    7. Milgrom, Paul, 1981. "An Axiomatic Characterization of Common Knowledge," Econometrica, Econometric Society, vol. 49(1), pages 219-222, January.
    8. Monderer, Dov & Samet, Dov, 1989. "Approximating common knowledge with common beliefs," Games and Economic Behavior, Elsevier, vol. 1(2), pages 170-190, June.
    9. Robert J Aumann, 1999. "Agreeing to Disagree," Levine's Working Paper Archive 512, David K. Levine.
    10. John Geanakoplos, 1992. "Common Knowledge," Journal of Economic Perspectives, American Economic Association, vol. 6(4), pages 53-82, Fall.
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    Cited by:

    1. Chichilnisky, Graciela, 1996. "Limited arbitrage is necessary and sufficient for the non-emptiness of the core," Economics Letters, Elsevier, vol. 52(2), pages 177-180, August.
    2. Joseph M. Ostroy, 1995. "Arbitrage of the Flattening Effect of Large Numbers," UCLA Economics Working Papers 737, UCLA Department of Economics.

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