题  目：Shapley’s Conjecture on the Cores of Abstract Market Games

报告人：曹志刚，中科院数学与系统科学院

时   间：2016年11月17日 9:30-11:00

地   点：知新楼B座1032

摘   要：

Shapley, L. S. (1955)  proposes a conjecture that all abstract market games possess cores, and their solutions are always connected sets meeting the “A” and “B” faces of the imputation simplex in single points. We show that Shapley’s conjecture is correct when n is less than 4. A dual-concave game  with specific assumptions has a nonempty core. In addition, the core has apolarized structure.