Cooperative games in permutational structure
By a cooperative game in coalitional structure or shortly coalitional game we mean the standard cooperative non-transferable utility game described by a set of payoffs for each coalition being a nonempty subset of the grand coalition of all players. It is well-known that balancedness is a sufficient condition for the nonemptiness of the core of such a cooperative non-transferable utility game. In this paper we consider non-transferable utility games in which for any coalition the set of payoffs depends on a permutation or ordering upon any partition of the coalition into subcoalitions. We call such a game a cooperative game in permutational structure or shortly permutational game. Doing so we extend the scope of the standard cooperative game theory in dealing with economic or political problems. Next we define the concept of core for such games. By introducing balancedness for ordered partitions of coalitions, we prove the nonemptiness of the core of a balanced non-transferable utility permutational game. Moreover we show that the core of a permutational game coincides with the core of an induced game in coalitional structure, but that balancedness of the permutational game need not imply balancedness of the corresponding coalitional game. This leads to a weakening of the conditions for the existence of a nonempty core of a game in coalitional structure, induced by a game in permutational structure. Furthermore, we refine the concept of core for the class of permutational games. We call this refinement the balanced-core of the game and show that the balanced-core of a balanced permutational game is a nonempty subset of the core. The proof of the nonemptiness of the core of a permutational game is based on a new intersection theorem on the unit simplex, which generalizes the well-known intersection theorem of Shapley.
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.
Volume (Year): 11 (1998)
Issue (Month): 2 ()
|Note:||Received: October 31, 1995; revised version: February 5, 1997|
|Contact details of provider:|| Web page: http://link.springer.de/link/service/journals/00199/index.htm|
|Order Information:||Web: http://link.springer.de/orders.htm|
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Ichiishi, Tatsuro & Idzik, Adam, 1991. "Closed Covers of Compact Convex Polyhedra," International Journal of Game Theory, Springer, vol. 20(2), pages 161-69.
- Nowak Andrzej S. & Radzik Tadeusz, 1994. "The Shapley Value for n-Person Games in Generalized Characteristic Function Form," Games and Economic Behavior, Elsevier, vol. 6(1), pages 150-161, January.
When requesting a correction, please mention this item's handle: RePEc:spr:joecth:v:11:y:1998:i:2:p:427-442. 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 references are entirely missing, you can add them using this form.