On the mixed reduction: an alternative axiomatization of the fuzzy NTU core

Abstract

In the framework of fuzzy non-transferable-utility (NTU) games, Hwang [5], and Liao [6] introduced several extensions of reduced games and related consistency properties due to [3], Serrano and Volij [8] and Voorneveld and van den Nouweland [9], respectively. Different from the axiomatic results due to Hwang [5], and Liao [6], this paper is devoted to propose a mixed reduction and related consistency property to characterize the core on fuzzy non-transferable-utility (NTU) games. .

Keywords

• fuzzy NTU game
• the core
• reduction

References

1. [1] J.P. Aubin, Coeur et valeur des jeux flous á paiements latéraux, Comptes Rendus de l’Académie des Sciences 279:891-894, (1974)
2. [2] J.P. Aubin, Cooperative fuzzy games, Mathematics of Operations Research 6:1-13, (1981)
3. [3] Davis M, Maschler M (1965) The kernel of a cooperative game. Naval Research Logistics Quarterly 12:223-259
4. [4] J.C. Harsanyi, A bargaining model for the cooperative n-person game, In Contributions to the Theory of Games IV (Annals of Mathematics Studies 40), e.d. by A.w. Tucker and R.D. Luce Princeton: Princeton University Press, 325–355, (1959)
5. [5] Y.A. Hwang, Fuzzy games: a characterization of the core, Fuzzy Sets and Systems 158:2480-2493, (2007)
6. [6] Y.H. Liao, Consistency and the core for fuzzy non-transferable-utility games. Economics Bulletin 3(45):1-6, (2008)
7. [7] B. Peleg, An axiomatization of the core of cooperative games without side payments. Journal of Mathematical Economics, 14:203–214, (1985)
8. [8] R. Serrano, O. Volij, Axiomatizations of neoclassical concepts for economies. Journal of Mathematical Economics 30:87–108, (1998)

9. [9] M. Voorneveld, A. van den Nouweland, A new axiomatization of the core of games with transferable utility. Economics Letters, 60:151–155, (1998)