IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this article or follow this journal

An Equilibrium-Point Interpretation of Stable Sets and a Proposed Alternative Definition

  • John C. Harsanyi

    (University of California, Berkeley)

The paper argues that the von Neumann-Morgenstern definition of stable sets is unsatisfactory because it neglects the destabilizing effect of indirect dominance relations. This argument is supported both by heuristic considerations and by construction of a bargaining game B(G), formalizing the bargaining process by which the players agree on their payoffs from an n-person cooperative game G. (G itself is assumed to be given in characteristic-function form allowing side payments.) The strategies \rho i , the players use in this bargaining game will determine which payoff vectors x will be stationary, i.e., will have the property that, should such a payoff vector x be proposed to the players, all further bargaining will stop and x will be accepted as the outcome of the game. It will be suggested that a stable set should be defined as the set V of all stationary payoff vectors x, on the assumption that the players' bargaining strategies p, will form a canonical equilibrium point \rho in the bargaining game B(G). In a certain class of games, to be called absolutely stable games, indirect dominance relations turn out to be irrelevant, and in these games the suggested definition for stable sets is equivalent to the von Neumann-Morgenstern definition. But in general this is not the case. However, if we assume that the players will adopt bargaining strategies deliberately discouraging any use of indirect dominance relations, then, in every game, the stable sets our model yields will always be von Neumann-Morgenstern stable sets. At the end of the paper, we briefly discuss a possible modification in the suggested definition for stable sets, based on a modified bargaining game B 0(G), in which the players are permitted to accept cuts in their provisional payoffs if they think that this move will increase their final payoffs.

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.

File URL: http://dx.doi.org/10.1287/mnsc.20.11.1472
Download Restriction: no

Article provided by INFORMS in its journal Management Science.

Volume (Year): 20 (1974)
Issue (Month): 11 (July)
Pages: 1472-1495

as
in new window

Handle: RePEc:inm:ormnsc:v:20:y:1974:i:11:p:1472-1495
Contact details of provider: Postal: 7240 Parkway Drive, Suite 300, Hanover, MD 21076 USA
Phone: +1-443-757-3500
Fax: 443-757-3515
Web page: http://www.informs.org/
Email:


More information through EDIRC

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

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

When requesting a correction, please mention this item's handle: RePEc:inm:ormnsc:v:20:y:1974:i:11:p:1472-1495. 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: (Mirko Janc)

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.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.