On the Interval Game-Theoretic Solutions and Their Axiomatizations

Osman Palancıй osmanpalanci [at] sdu.edu.tr
Sırma Zeynep Alparslan Gök2 sirmagok [at] sdu.edu.tr
Ayşen Gül Yılmaz Büyükyağcı3 arslan576 [at] hotmail.com
  1. Department of Mathematics, Faculty of Arts and Sciences, Süleyman Demirel University, 32260 Isparta, Turkey
  2. Department of Mathematics, Faculty of Arts and Sciences, Süleyman Demirel University, 32260 Isparta, Turkey
  3. Department of Mathematics, Faculty of Arts and Sciences, Süleyman Demirel University, 32260 Isparta, Turkey
Abstract 

Natural questions for people or businesses that face interval uncertainty in their data when dealing with cooperation are: Which coalitions should form? How to distribute the collective gains or costs? The theory of cooperative interval games is a suitable tool for answering these questions. In this paper, we introduced and characterizated the new interval solutions concepts, i.e. interval CIS-value, interval ENSC-value and interval equal division solution by using cooperative interval games. Finally, we characterizd these interval solutions for two-player games

References 

[1] Alparslan Gök, S.Z., Branzei, R., Tijs, S., 2009.
Convex Interval Games. Journal of Applied
Mathematics and Decision Sciences, Article ID
342089, 14 pages.
INTERNATIONAL YOUTH SCIENCE FORUM “LITTERIS ET ARTIBUS”, 24–26 NOVEMBER 2016, 70 LVIV, UKRAINE
[2] Alparslan Gök, S.Z., Branzei, R., Tijs, S., 2010. The interval Shapley value: an axiomatization. Central Euro-pean Journal of Operations Research, 18(2), 131-140.
[3] Alparslan Gök, S.Z., Miquel, S., Tijs, S., 2009. Cooperation under interval uncertainty. Mathematical Methods of Operations Research, 69, 99-109.
[4] Branzei, R., Dimitrov, D., Tijs, S., 2008. Models in Cooperative Game Theory. Springer-Verlag, 204 pages, Berlin.
[5] Driessen, T.S.H., Funaki, Y., 1991. Coincidence of and collinearity between game theoretic solutions. OR Spektrum, 13, 15-30.
[6] Hans, P., 2008. Game Theory: A Multi-Leveled Approach. Springer-Verlag, Berlin Heidelberg, 494 pages, Berlin.
[7] Moore, R., 1979. Methods and Applications of Interval Analysis. SIAM Studies in Applied Mathematics, 190 pages, Philadelphia.
[8] Shapley, L.S., 1953. A value for n-person games. Annals of Mathematics Studies, 28, 307-317.
[9] van den Brink, R., Funaki, Y., 2009. Axiomatizations of a class of equal surplus sharing solutions for cooperative games with transferable utility, Theory and Decision, 67, 303-340.