Vertical Syndication-Proof Competitive Prices in Multilateral Markets
AbstractA 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 InfoPaper provided by Universitat de Barcelona. Espai de Recerca en Economia in its series Working Papers in Economics with number 283.
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Date of creation: 2012
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Find related papers by JEL classification:
- C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
- D43 - Microeconomics - - Market Structure and Pricing - - - Oligopoly and Other Forms of Market Imperfection
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-11-11 (All new papers)
- NEP-COM-2012-11-11 (Industrial Competition)
- NEP-IND-2012-11-11 (Industrial Organization)
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