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Vertical Syndication-Proof Competitive Prices in Multilateral Markets

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  • O. Tejada and M. Alvarez-Mozos

    (Universitat de Barcelona)

Abstract

A multi-sided Bohm-Bawerk assignment game (Tejada, to appear) is a model for a multilateral market with a finite number of perfectly complementary indivisible com- modities owned by different sellers, and inflexible demand and support functions. We show that for each such market game there is a unique vector of competitive prices for the commodities that is vertical syndication-proof, in the sense that, at those prices, syndication of sellers each owning a different commodity is neither beneficial nor detri- mental for the buyers. Since, moreover, the benefits obtained by the agents at those prices correspond to the nucleolus of the market game, we provide a syndication-based foundation for the nucleolus as an appropriate solution concept for market games. For different solution concepts a syndicate can be disadvantageous and there is no escape to Aummans paradox (Aumann, 1973). We further show that vertical syndication- proofness and horizontal syndication-proofness in which sellers of the same commod- ity collude are incompatible requirements under some mild assumptions. Our results build on a self-interesting link between multi-sided Bohm-Bawerk as- signment games and bankruptcy games (ONeill, 1982). We identify a particular subset of Bohm-Bawerk assignment games and we show that it is isomorphic to the whole class of bankruptcy games. This isomorphism enables us to show the uniqueness of the vec- tor of vertical syndication-proof prices for the whole class of Bohm-Bawerk assignment market using well-known results of bankruptcy problems.

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Bibliographic Info

Paper provided by Universitat de Barcelona. Espai de Recerca en Economia in its series Working Papers in Economics with number 283.

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Length: 0 pages
Date of creation: 2012
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Handle: RePEc:bar:bedcje:2012283

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Postal: Espai de Recerca en Economia, Facultat de Ciències Econòmiques. Tinent Coronel Valenzuela, Num 1-11 08034 Barcelona. Spain.
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References

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  1. Guesnerie, Roger, 1977. "Monopoly, syndicate, and shapley value: About some conjectures," Journal of Economic Theory, Elsevier, Elsevier, vol. 15(2), pages 235-251, August.
  2. Patrick Legros, 1987. "Disadvantageous syndicates and stable cartels: the case of the nucleolus," ULB Institutional Repository 2013/7046, ULB -- Universite Libre de Bruxelles.
  3. Andrew Postlewaite, 1974. "Disadvantageous Syndicates in Exchange Economies," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 105, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  4. Postlewaite, Andrew & Rosenthal, Robert W., 1974. "Disadvantageous syndicates," Journal of Economic Theory, Elsevier, Elsevier, vol. 9(3), pages 324-326, November.
  5. Salant, Stephen W & Switzer, Sheldon & Reynolds, Robert J, 1983. "Losses from Horizontal Merger: The Effects of an Exogenous Change in Industry Structure on Cournot-Nash Equilibrium," The Quarterly Journal of Economics, MIT Press, MIT Press, vol. 98(2), pages 185-99, May.
  6. Aumann, Robert J., 1973. "Disadvantageous monopolies," Journal of Economic Theory, Elsevier, Elsevier, vol. 6(1), pages 1-11, February.
  7. Aumann, Robert J. & Maschler, Michael, 1985. "Game theoretic analysis of a bankruptcy problem from the Talmud," Journal of Economic Theory, Elsevier, Elsevier, vol. 36(2), pages 195-213, August.
  8. Oriol Tejada & Carles Rafels, 2010. "Symmetrically multilateral-bargained allocations in multi-sided assignment markets," International Journal of Game Theory, Springer, Springer, vol. 39(1), pages 249-258, March.
  9. Shapley, Lloyd S. & Shubik, Martin, 1969. "On market games," Journal of Economic Theory, Elsevier, Elsevier, vol. 1(1), pages 9-25, June.
  10. Oriol Tejada, 2010. "A note on competitive prices in multilateral assignment markets," Economics Bulletin, AccessEcon, vol. 30(1), pages 658-662.
  11. Thomson, William, 2003. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: a survey," Mathematical Social Sciences, Elsevier, Elsevier, vol. 45(3), pages 249-297, July.
  12. Okuno, Masahiro & Postlewaite, Andrew & Roberts, John, 1980. "Oligopoly and Competition in Large Markets," American Economic Review, American Economic Association, American Economic Association, vol. 70(1), pages 22-31, March.
  13. Quint, Thomas, 1991. "The core of an m-sided assignment game," Games and Economic Behavior, Elsevier, Elsevier, vol. 3(4), pages 487-503, November.
  14. Gardner, Roy, 1977. "Shapley value and disadvantageous monopolies," Journal of Economic Theory, Elsevier, Elsevier, vol. 16(2), pages 513-517, December.
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Cited by:
  1. Tejada, J. & Borm, P.E.M. & Lohmann, E.R.M.A., 2013. "A Unifying Model for Matching Situations," Discussion Paper, Tilburg University, Center for Economic Research 2013-069, Tilburg University, Center for Economic Research.

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