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Efficiency under a combination of ordinal and cardinal information on preferences

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  • Athanassoglou, Stergios

Abstract

Abstract Consider a collection of m indivisible objects to be allocated to n agents, where m>=n. Each agent falls in one of two distinct categories: either he (a) has a complete ordinal ranking over the set of individual objects, or (b) has a set of "plausible" benchmark von Neumann-Morgenstern (vNM) utility functions in whose positive span his "true" utility is known to lie. An allocation is undominated if there does not exist a preference-compatible profile of vNM utilities at which it is Pareto dominated by another feasible allocation. Given an undominated allocation, we use the tools of linear duality theory to construct a profile of vNM utilities at which it is ex-ante welfare maximizing. A finite set of preference-compatible vNM utility profiles is exhibited such that every undominated allocation is ex-ante welfare maximizing with respect to at least one of them. Given an arbitrary allocation, we provide an interpretation of the constructed vNM utilities as subgradients of a function which measures worst-case domination.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Mathematical Economics.

Volume (Year): 47 (2011)
Issue (Month): 2 (March)
Pages: 180-185

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Handle: RePEc:eee:mateco:v:47:y:2011:i:2:p:180-185

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Web page: http://www.elsevier.com/locate/jmateco

Related research

Keywords: Random assignment Efficiency Duality Linear programming;

References

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  1. Bogomolnaia, Anna & Moulin, Herve, 2001. "A New Solution to the Random Assignment Problem," Journal of Economic Theory, Elsevier, Elsevier, vol. 100(2), pages 295-328, October.
  2. McLennan, Andrew, 2002. "Ordinal Efficiency and the Polyhedral Separating Hyperplane Theorem," Journal of Economic Theory, Elsevier, Elsevier, vol. 105(2), pages 435-449, August.
  3. Abdulkadiroglu, Atila & Sonmez, Tayfun, 2003. "Ordinal efficiency and dominated sets of assignments," Journal of Economic Theory, Elsevier, Elsevier, vol. 112(1), pages 157-172, September.
  4. Carroll, Gabriel, 2010. "An efficiency theorem for incompletely known preferences," Journal of Economic Theory, Elsevier, Elsevier, vol. 145(6), pages 2463-2470, November.
  5. Yeon-Koo Che & Fuhito Kojima, 2010. "Asymptotic Equivalence of Probabilistic Serial and Random Priority Mechanisms," Econometrica, Econometric Society, Econometric Society, vol. 78(5), pages 1625-1672, 09.
  6. Kesten, Onur, 2009. "Why do popular mechanisms lack efficiency in random environments?," Journal of Economic Theory, Elsevier, Elsevier, vol. 144(5), pages 2209-2226, September.
  7. Mihai Manea, 2008. "Random serial dictatorship and ordinally efficient contracts," International Journal of Game Theory, Springer, Springer, vol. 36(3), pages 489-496, March.
  8. Katta, Akshay-Kumar & Sethuraman, Jay, 2006. "A solution to the random assignment problem on the full preference domain," Journal of Economic Theory, Elsevier, Elsevier, vol. 131(1), pages 231-250, November.
  9. Manea, Mihai, 2008. "A constructive proof of the ordinal efficiency welfare theorem," Journal of Economic Theory, Elsevier, Elsevier, vol. 141(1), pages 276-281, July.
  10. Manea, Mihai, 2009. "Asymptotic ordinal inefficiency of random serial dictatorship," Theoretical Economics, Econometric Society, Econometric Society, vol. 4(2), June.
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