# American Institute of Mathematical Sciences

August & September  2019, 12(4&5): 1187-1198. doi: 10.3934/dcdss.2019082

## Cores and optimal fuzzy communication structures of fuzzy games

 1 School of Management, Qingdao University of Technology, Qingdao 266520, China 2 Business School, Central South University, Changsha 410083, China

* Corresponding author: Jiaquan Zhan

Received  June 2017 Revised  December 2017 Published  November 2018

In real game problems not all players can cooperate directly, games with communication structures introduced by Myerson in 1977 can deal with these problems quite well. More recently, this concept has been introduced into fuzzy games. In this paper, games on (fuzzy) communication structures were studied. We proved that if a coalitional game has a nonempty core, then the game restricted on an n-person connected graph also has a nonempty core. Further, the fuzzy game restricted on the n-person connected graph also has a nonempty core. Moreover, we proved the above two cores are identical and the core of the coalitional game is included in them. In addition, optimal fuzzy communication structures of fuzzy games were studied. We showed that the optimal communication structures do exist and proposed three allocating methods. In the end, a full illustrating example was given.

Citation: Jiaquan Zhan, Fanyong Meng. Cores and optimal fuzzy communication structures of fuzzy games. Discrete & Continuous Dynamical Systems - S, 2019, 12 (4&5) : 1187-1198. doi: 10.3934/dcdss.2019082
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