# On the Set of Proper Equilibria of a Bimatrix Game

## Author

Listed:
• Jansen, Mathijs

## Abstract

In this paper it is proved that the set of proper equilibria of a bimatrix game is the finite union of polytopes. To that purpose we split up the strategy space of each player into a finite number of equivalence classes and consider for a given [epsilon] [greater than] 0 the set of all [epsilon]-proper pairs within the cartesian product of two equivalence classes. If this set is non-empty, its closure is a polytope. By considering this polytope as [epsilon] goes to zero, we obtain a (Myerson) set of proper equilibria. A Myerson set appears to be a polytope.

## Suggested Citation

• Jansen, Mathijs, 1993. "On the Set of Proper Equilibria of a Bimatrix Game," International Journal of Game Theory, Springer;Game Theory Society, vol. 22(2), pages 97-106.
• Handle: RePEc:spr:jogath:v:22:y:1993:i:2:p:97-106
as

To our knowledge, this item is not available for download. To find whether it is available, there are three options:
1. Check below whether another version of this item is available online.
2. Check on the provider's web page whether it is in fact available.
3. Perform a search for a similarly titled item that would be available.

## References listed on IDEAS

as
1. Kreps, David M & Wilson, Robert, 1982. "Sequential Equilibria," Econometrica, Econometric Society, vol. 50(4), pages 863-894, July.
2. Okada, A, 1988. "Perfect Equilibrium Points and Lexicographic Domination," International Journal of Game Theory, Springer;Game Theory Society, vol. 17(3), pages 225-239.
Full references (including those not matched with items on IDEAS)

## Citations

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

Cited by:

1. Kleppe, John & Borm, Peter & Hendrickx, Ruud, 2012. "Fall back equilibrium," European Journal of Operational Research, Elsevier, vol. 223(2), pages 372-379.
2. Fiestras-Janeiro, G. & Borm, P.E.M. & van Megen, F.J.C., 1996. "Protective Behavior in Games," Discussion Paper 1996-12, Tilburg University, Center for Economic Research.
3. Dieter Balkenborg & Josef Hofbauer & Christoph Kuzmics, 2015. "The refined best-response correspondence in normal form games," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(1), pages 165-193, February.
4. repec:spr:compst:v:78:y:2013:i:2:p:171-186 is not listed on IDEAS
5. John Kleppe & Peter Borm & Ruud Hendrickx, 2013. "Fall back equilibrium for $$2 \times n$$ bimatrix games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 78(2), pages 171-186, October.

## Corrections

All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:jogath:v:22:y:1993:i:2:p:97-106. 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: (Sonal Shukla) or (Rebekah McClure). General contact details of provider: http://www.springer.com .

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.

We have no references for this item. You can help adding them by using 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 RePEc Author Service 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.

IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.