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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.

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Bibliographic Info

Paper provided by EconWPA in its series Game Theory and Information with number 0512002.

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Date of creation: 10 Dec 2005
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Handle: RePEc:wpa:wuwpga:0512002

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Web page: http://128.118.178.162

Related research

Keywords: social choice; outcome function; efficient; consistent; converse consistent;

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  1. Somdeb Lahiri, 2005. "Manipulation via Endowments in a Market with Profit Maximizing Agents," Game Theory and Information 0511008, EconWPA.
  2. Moulin, H & Thomson, W, 1995. "Axiomatic Analysis of Resource Allocation," RCER Working Papers 400, University of Rochester - Center for Economic Research (RCER).
  3. Carmen Bevia, 1996. "Identical preferences lower bound solution and consistency in economies with indivisible goods," Social Choice and Welfare, Springer, vol. 13(1), pages 113-126, January.
  4. Ergin, Haluk I., 2000. "Consistency in house allocation problems," Journal of Mathematical Economics, Elsevier, vol. 34(1), pages 77-97, August.
  5. Shapley, Lloyd S. & Shubik, Martin, 1969. "On market games," Journal of Economic Theory, Elsevier, vol. 1(1), pages 9-25, June.
  6. Tadenuma, Koichi & Thomson, William, 1991. "No-Envy and Consistency in Economies with Indivisible Goods," Econometrica, Econometric Society, vol. 59(6), pages 1755-67, November.
  7. Zaifu YANG & Ning SUN, 2004. "The Max-Convolution Approach to Equilibrium Models with Indivisibilities," Econometric Society 2004 Far Eastern Meetings 564, Econometric Society.
  8. Hurwicz, Leonid, 1973. "The Design of Mechanisms for Resource Allocation," American Economic Review, American Economic Association, vol. 63(2), pages 1-30, May.
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