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

## Author Info

• Diego Moreno

()

• 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)

## 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.

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## Bibliographic Info

Article provided by Springer & Game Theory Society in its journal International Journal of Game Theory.

Volume (Year): 28 (1999)
Issue (Month): 1 ()
Pages: 1-14

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 Handle: RePEc:spr:jogath:v:28:y:1999:i:1:p:1-14 Note: Received May 1998/Revised version September 1998 Contact details of provider: Web page: http://www.springer.com Order Information: Web: http://www.springer.com/economics/economic+theory/journal/182/PS2

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