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Vertical Syndication-Proof Competitive Prices in Multilateral Markets

  • O. Tejada and M. Alvarez-Mozos

    (Universitat de Barcelona)

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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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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  1. Oriol Tejada, 2010. "A note on competitive prices in multilateral assignment markets," Economics Bulletin, AccessEcon, vol. 30(1), pages 658-662.
  2. Legros, Patrick, 1987. "Disadvantageous syndicates and stable cartels: The case of the nucleolus," Journal of Economic Theory, Elsevier, vol. 42(1), pages 30-49, June.
  3. Postlewaite, Andrew & Rosenthal, Robert W., 1974. "Disadvantageous syndicates," Journal of Economic Theory, Elsevier, vol. 9(3), pages 324-326, November.
  4. Guesnerie, Roger, 1977. "Monopoly, syndicate, and shapley value: About some conjectures," Journal of Economic Theory, Elsevier, vol. 15(2), pages 235-251, August.
  5. Okuno, Masahiro & Postlewaite, Andrew & Roberts, John, 1980. "Oligopoly and Competition in Large Markets," American Economic Review, American Economic Association, vol. 70(1), pages 22-31, March.
  6. Aumann, Robert J. & Maschler, Michael, 1985. "Game theoretic analysis of a bankruptcy problem from the Talmud," Journal of Economic Theory, Elsevier, vol. 36(2), pages 195-213, August.
  7. Shapley, Lloyd S. & Shubik, Martin, 1969. "On market games," Journal of Economic Theory, Elsevier, vol. 1(1), pages 9-25, June.
  8. Oriol Tejada & Carles Rafels, 2010. "Symmetrically multilateral-bargained allocations in multi-sided assignment markets," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(1), pages 249-258, March.
  9. Gardner, Roy, 1977. "Shapley value and disadvantageous monopolies," Journal of Economic Theory, Elsevier, vol. 16(2), pages 513-517, December.
  10. Aumann, Robert J., 1973. "Disadvantageous monopolies," Journal of Economic Theory, Elsevier, vol. 6(1), pages 1-11, February.
  11. Andrew Postlewaite, 1974. "Disadvantageous Syndicates in Exchange Economies," Discussion Papers 105, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  12. Quint, Thomas, 1991. "The core of an m-sided assignment game," Games and Economic Behavior, Elsevier, vol. 3(4), pages 487-503, November.
  13. Thomson, William, 2003. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: a survey," Mathematical Social Sciences, Elsevier, vol. 45(3), pages 249-297, July.
  14. Stephen W. Salant & Sheldon Switzer & Robert J. Reynolds, 1983. "Losses From Horizontal Merger: The Effects of an Exogenous Change in Industry Structure on Cournot-Nash Equilibrium," The Quarterly Journal of Economics, Oxford University Press, vol. 98(2), pages 185-199.
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