Irrational-Behavior-Proof Conditions Based on Limit Characteristic Functions
Cui LIU1, Hongwei GAO2, Ovanes PETROSIAN3, Juan XUE1, Lei WANG2
1. School of Mathematics and Statistics, Qingdao University, Qingdao 266071, China;
2. School of Mathematics and Statistics, Institute of Applied Mathematics of Shandong, Qingdao University, Qingdao 266071, China;
3. Faculty of Applied Mathematics and Control Processes, Saint Petersburg State University, Saint Petersburg, 198504, Russia
Irrational-behavior-proof (IBP) conditions are important aspects to keep stable cooperation in dynamic cooperative games. In this paper, we focus on the establishment of IBP conditions. Firstly, the relations of three kinds of IBP conditions are described. An example is given to show that they may not hold, which could lead to the fail of cooperation. Then, based on a kind of limit characteristic function, all these conditions are proved to be true along the cooperative trajectory in a transformed cooperative game. It is surprising that these facts depend only upon the individual rationalities of players for the Shapley value and the group rationalities of players for the core. Finally, an illustrative example is given.
This research was supported by National Natural Science Foundation of China (71571108), Projects of International (Regional) Cooperation and Exchanges of NSFC (71611530712, 61661136002), China Postdoctoral Science Foundation Funded Project (2016M600525), Qingdao Postdoctoral Application Research Project (2016029)
Corresponding Authors: Lei WANG
Cite this article:
Cui LIU,Hongwei GAO,Ovanes PETROSIAN et al. Irrational-Behavior-Proof Conditions Based on Limit Characteristic Functions[J]. Journal of Systems Science and Information, 2019, 7(1): 1-16.