INSTITUTE OF MATHEMATICAL ECONOMICS

Joachim Rosenmüller

Working-Paper No. 318

April 2000

Abstract

We discuss large but finite linear production games or market games. These games represent markets such that the agents decompose into finitely many disjoint groups each of which holds a corner of the market. In such a market most solution concepts like the core, the Shapley value, or the Walrasian equilibrium tend to favor the short side of the market excessively. That is, in the replicated limit or in the continuum version, the short side is awarded all the possible profits even though cooperation within the grand coalition is required. This kind of behavior is also observed with the Walrasian equilibrium. We show that vNM--Stable Sets differ markedly. For large but finite player sets we demonstrate that this concept is capable of assigning considerable profits towards the long side of the market. Also, it turns out that the shape of the generic vNM--Stable Set suggests cartelization of the market. Thus, it turns out that the long side first agrees to form a cartel and then forces the short side to make concessions. This way the long side profits from the game as well.

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