# 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 Âµ where Âµ 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.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

## Bibliographic Info

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

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

as in new window
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:

Order Information:

## Related research

Keywords: Coalitional game · core · non-atomic games;

## References

No references listed on IDEAS
You can help add them by filling out this form.

## Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
as in new window

Cited by:
1. Luigi Montrucchio & Marco Scarsini, 2005. "Large Newsvendor Games," Carlo Alberto Notebooks 15, Collegio Carlo Alberto.
2. Haimanko, Ori & Le Breton, Michel & Weber, Shlomo, 2004. "Voluntary formation of communities for the provision of public projects," Journal of Economic Theory, Elsevier, vol. 115(1), pages 1-34, March.
3. Massimiliano Amarante & Luigi Montrucchio, 2007. "Mas-Colell Bargaining Set of Large Games," Carlo Alberto Notebooks 63, Collegio Carlo Alberto.
4. Massimiliano Amarante & F. Maccheroni & M. Marinacci & L. Montrucchio, 2005. "Cores of non-atomic market games," Discussion Papers 0506-10, Columbia University, Department of Economics.
5. Massimo Marinacci & Luigi Montrucchio, 2001. "Subcalculus for set functions and cores of TU games," ICER Working Papers - Applied Mathematics Series 09-2001, ICER - International Centre for Economic Research.
6. Einy, Ezra & Moreno, Diego & Shitovitz, Benyamin, 1999. "The Asymptotic Nucleolus of Large Monopolistic Market Games," Journal of Economic Theory, Elsevier, vol. 89(2), pages 186-206, December.
7. Epstein, Larry G. & Marinacci, Massimo, 2001. "The Core of Large Differentiable TU Games," Journal of Economic Theory, Elsevier, vol. 100(2), pages 235-273, October.
8. Larry G. Epstein & Massimo Marinacci, 2000. "The Core of Large TU Games," RCER Working Papers 469, University of Rochester - Center for Economic Research (RCER).
9. Farhad Hüsseinov & Nobusumi Sagara, 2013. "Existence of efficient envy-free allocations of a heterogeneous divisible commodity with nonadditive utilities," Social Choice and Welfare, Springer, vol. 41(4), pages 923-940, October.

## Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

## Corrections

When requesting a correction, please mention this item's handle: RePEc:spr:jogath:v:28:y:1999:i:1:p:1-14. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Guenther Eichhorn) or (Christopher F Baum).

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.