A unifying model for matrix-based pairing situations |
| |
| Institution: | 1. CER—ETH Center of Economic Research, ETH Zurich, Switzerland;2. CentER and Department of Econometrics and Operations Research, Tilburg University, Netherlands;3. Quintiq Inc., United States;1. NICTA and UNSW, 223 Anzac Parade, Sydney, NSW 2033, Australia;2. School of Information Technologies, The University of Sydney, Australia;1. Advanced Teachers’ Training College, PO 47, Yaounde, Cameroon;2. Research and Training Unit for Doctorate in Mathematics, Computer Sciences and Applications, University of Yaounde I, P.O. Box 812, Yaounde, Cameroon;1. Faculty of Economics, Takasaki City University of Economics, 1300 Kaminamie, Takasaki, Gunma 370-0801, Japan;2. Institute of Social Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan;3. Faculty of Economics, Sophia University, 7-1 Kioi-cho, Chiyoda-ku, Tokyo 102-8554, Japan;1. Department of Economics, Seoul National University, Seoul, South Korea;2. Economic Research Unit, Indian Statistical Institute, Kolkata, India;3. Department of Economics, University of Leicester, Leicester, United Kingdom;1. College of Resources and Environmental Sciences, Nanjing Agricultural University, Nanjing, Jiangsu 210095, China;2. State Key Laboratory of Vegetation and Environmental Change, Institute of Botany, Chinese Academy of Sciences, Beijing 100093, China |
| |
| Abstract: | We present a unifying framework for transferable utility coalitional games that are derived from a non-negative matrix in which every entry represents the value obtained by combining the corresponding row and column. We assume that every row and every column is associated with a player, and that every player is associated with at most one row and at most one column. The instances arising from this framework are called pairing games, and they encompass assignment games and permutation games as two polar cases. We show that the core of a pairing game is always non-empty by proving that the set of pairing games coincides with the set of permutation games. Then we exploit the wide range of situations comprised in our framework to investigate the relationship between pairing games that have different player sets, but are defined by the same underlying matrix. We show that the core and the set of extreme core allocations are immune to the merging of a row player with a column player. Moreover, the core is also immune to the reverse manipulation, i.e., to the splitting of a player into a row player and a column player. Other common solution concepts fail to be either merging-proof or splitting-proof in general. |
| |
| Keywords: | |
| 本文献已被 ScienceDirect 等数据库收录！ |
|
