The core of a class of non-atomic games which arise in economic applications

We study the core of a non-atomic game v which is uniformly continuous with respect to the DNA-topology and continuous at the grand coalition. Such a game has a unique DNA-continuous extension on the space B ₁ of ideal sets. We show that if the extension is concave then the core of the game v is non-empty iff is homogeneous of degree one along the diagonal of B ₁. We use this result to obtain representation theorems for the core of a non-atomic game of the form v=f^μ where μ is a finite dimensional vector of measures and f is a concave function. We also apply our results to some non-atomic games which occur in economic applications.

Authors and Affiliations

1. Department of Economics, Ben-Gurion University of the Negev, Beer Sheva 84105, Israel (e-mail: einy@bgumail.bgu.ac.il), , , , , , IL

   Ezra Einy

2. Departmento de Economia, Universidad Carlos III de Madrid, E-28903 Getafe, Spain (e-mail: dmoreno@eco.uc3m.es), , , , , , ES

   Diego Moreno

3. Department of Economics, University of Haifa, Mount Carmel, Haifa 31905, Israel (e-mail: binya@econ.haifa.ac.il), , , , , , IL

   Benyamin Shitovitz

Received May 1998/Revised version September 1998

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