A partition-graph restricted cooperative game with incomplete information

¹ School of Logistics, Beijing Wuzi University, Tongzhou, Beijing, P.R. China
² Worley, Chaoyang, Beijing 100012, P.R. China
³ Capital University of Economics and Business, Fengtai, Beijing, P.R. China

^* Corresponding author: yuxiaohui513@163.com

Received: 24 December 2023
Accepted: 8 June 2024

Abstract

In a partition-graph restricted cooperative game with incomplete information, it is assumed that a prior coalition takes part in the grand coalition N in form of communication structure. Before the grand coalition is formed, all the players participate in the cooperation just by communication structure. Hence, a new cooperative game with communication structure (a restricted game for short) is formed. In this study, a new value of a restricted game is proposed, which is defined by the Myserson value and the Shapley value. It is proved that the added value of grand coalition is distributed by a certain ratio (i.e., the Shapley value). By generalized the distribution ratio, a further extension of the proposed value is gotten, i.e., the weight extended value. This weight extended value is unique based on restricted component efficiency, weight fairness, weight symmetric across coalitions, null coalition property and restricted linearity.