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

Diego Moreno (), Benyamin Shitovitz () and Ezra Einy ()
Benyamin Shitovitz: Department of Economics, University of Haifa, Mount Carmel, Haifa 31905, Israel
Ezra Einy: Department of Economics, Ben-Gurion University of the Negev, Beer Sheva 84105, Israel

International Journal of Game Theory, 1999, vol. 28, issue 1, 1-14

Abstract: 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 ${\overline {v}}$ on the space B1 of ideal sets. We show that if the extension ${\overline {v}}$ is concave then the core of the game v is non-empty iff ${\overline {v}}$ is homogeneous of degree one along the diagonal of B1. We use this result to obtain representation theorems for the core of a non-atomic game of the form v=fˆ 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.

Keywords: Coalitional; game; ·; core; ·; non-atomic; games (search for similar items in EconPapers)
Date: 1999-02-11
Note: Received May 1998/Revised version September 1998
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