Self-duality of solutions in cooperative games
By: Kensaku Kikuta
Series: Working paper -- no. 189; Working paper (Kōbe Shōka Daigaku. Keizai Kenkyūjo) -- no. 189
Publisher: Institute of Economic Research, Kobe University of Commerce
Published: 2002
Place of publication: Kobe
Language: eng
Number of pages: 12
Subjects: Game theory; Bankruptcy; Mathematical models; Duality theory (Mathematics)
Description: In this paper we extend the self-duality of a rule in a bankruptcy problem to a property (we call this the self-duality) of a solution-concept in coalitional games. First, we define a new coalitional game, corresponding to an original coalitional game. When the original game is associated with a bankruptcy problem, the new coalitional game corresponds to the bankruptcy problem which appears in the dual rule. Then we define the dual of a solution-concept, using the new coalitional game. Then we define the self-duality of a solution-concept. When original games are associated with bankruptcy problems, the dual solution and the self-duality correspond to the dual rule and self-duality of rules in bankruptcy problems. We show both the Shapely value and the prenucleolus have the self-duality. Furthermore, we see the self-duality is closely related to the negative duality of a solution-concept.-p.1.
Notes: "February 2002."

Includes bibliographical references (leaves 11-12).