No Access

Alternative Reductions and Axiomatizations of the Unit-Level-Core

Ling-Yun Chung

Graduate School of Technological and Vocational Education, National Yunlin University of Science and Technology, Taiwan

E-mail Address: darlingyun@gmail.com

Search for more papers by this author

Yu-Hsien Liao

Department of Applied Mathematics, National Pingtung University, Pingtung City, Pingtung, Taiwan

E-mail Address: twincos@ms25.hinet.net

Corresponding author.

Search for more papers by this author

Wen-Ying Hsieh

Graduate School of Technological and Vocational Education, National Yunlin University of Science and Technology, Taiwan

E-mail Address: hsiehwy@yuntech.edu.tw

Search for more papers by this author

Tsu-Yin Chen

Graduate School of Technological and Vocational Education, National Yunlin University of Science and Technology, Taiwan

E-mail Address: tychen@gw.cgust.edu.tw

Search for more papers by this author

, and

Chen-Kun Lin

Graduate School of Technological and Vocational Education, National Yunlin University of Science and Technology, Taiwan

E-mail Address: cklin@hyivs.tnc.edu.tw

Search for more papers by this author

https://doi.org/10.1142/S0217595916500524Cited by:0 (Source: Crossref)

Abstract

By simultaneously considering both the players and the participation levels, we introduce two alternative definitions of the reduced games. Further, several axiomatizations of the unit-level-core are also obtained by applying related properties of consistency and its converse.

Keywords:

References

Davis, M and M Maschler (1965). The kernel of a cooperative game. Naval Research Logistics Quarterly, 12, 223–259. Crossref, Google Scholar
Hwang, YA and YH Liao (2010). The unit-level-core for multi-choice games: The replicated core for TU games. Journal of Global Optimization, 47, 161–171. Crossref, Web of Science, Google Scholar
Hwang, YA and P Sudhölter (2001). Axiomatizations of the core on the universal domain and other natural domains. International Journal of Game Theory, 29, 597–623. Crossref, Web of Science, Google Scholar
Liao, YH (2009). Moulin reduction, V-N reduction and axiomatizations of the duplicate core. Asia-Pacific Journal of Operational Research, 26, 623–636. Link, Web of Science, Google Scholar
Moulin, H (1985). The separability axiom and equal-sharing methods. Journal of Economic Theory, 36, 120–148. Crossref, Web of Science, Google Scholar
Nouweland A van den, Potters, J, S Tijs and J Zarzuelo (1995). Core and related solution concepts for multi-Choice games. ZOR-Mathematical Methods of Operations Research, 41, 289–311. Crossref, Google Scholar
Peleg, B (1985). An axiomatization of the core of cooperative games without side payments. Journal of Mathematical Economics, 14, 203–214. Crossref, Web of Science, Google Scholar
Peleg, B (1986). On the reduced game property and its converse. International Journal of Game Theory, 15, 187–200. Crossref, Google Scholar
Tadenuma, K (1992). Reduced Games, consistency, and the core. International Journal of Game Theory, 20, 325–334. Crossref, Web of Science, Google Scholar