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Consistency and the Competitive Outcome Function

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  • Somdeb Lahiri

    (Institute for Financial Management & Research)

Abstract

In this paper we are interested in the social choice theory of allocating resources, which are available and can be consumed in integer units only. Since goods are available in integer units only, the social choice theory for such problems cannot exploit any smoothness property, which may otherwise have been embedded in the preferences of the agents. This makes the outcome function approach for the study of such problems quite compelling. Our purpose here is to study outcome functions, which are efficient and consistent. We provide an example to show that the competitive social choice function may not be converse consistent. The competitive outcome function is easily observed to be efficient, consistent and converse consistent. What we are able to show here is that any efficient and consistent outcome function which is “reasonably well-behaved” for two-agent problems, must be a sub-correspondence of the competitive outcome function. Our proof of this result requires the converse consistency of the competitive outcome function.

Suggested Citation

  • Somdeb Lahiri, 2005. "Consistency and the Competitive Outcome Function," Game Theory and Information 0512002, University Library of Munich, Germany.
    • Handle: RePEc:wpa:wuwpga:0512002
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    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/game/papers/0512/0512002.pdf
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    References listed on IDEAS

    as
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    5. Campbell,Donald E., 1987. "Resource Allocation Mechanisms," Cambridge Books, Cambridge University Press, number 9780521319904, January.
    6. Somdeb Lahiri, 2005. "Manipulation via Endowments in a Market with Profit Maximizing Agents," Game Theory and Information 0511008, University Library of Munich, Germany.
    7. Carmen Bevia, 1996. "Identical preferences lower bound solution and consistency in economies with indivisible goods," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 13(1), pages 113-126, January.
    8. Ergin, Haluk I., 2000. "Consistency in house allocation problems," Journal of Mathematical Economics, Elsevier, vol. 34(1), pages 77-97, August.
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    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    social choice; outcome function; efficient; consistent; converse consistent;
    All these keywords.

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D8 - Microeconomics - - Information, Knowledge, and Uncertainty

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