Public resources allocation using an uncertain cooperative game among vulnerable groups

This paper aims to solve the problem of public resource allocation among vulnerable groups by proposing a new method called uncertain α-coordination value based on uncertain cooperative game.

First, explicit forms of uncertain Shapley value with Chouqet integral form and uncertain centre-of-gravity of imputation-set (CIS) value are defined separately on the basis of uncertainty theory and cooperative game. Then, a convex combination of the two values above called the uncertain α-coordination value is used as the best solution. This study proves that the proposed methods meet the basic properties of cooperative game.

The uncertain α-coordination value is used to solve a public medical resource allocation problem in fuzzy coalitions and uncertain payoffs. Compared with other methods, the α-coordination value can solve such problem effectively because it balances the worries of vulnerable group’s further development and group fairness.

In this paper, an extension of classical cooperative game called uncertain cooperative game is proposed, in which players choose any level of participation in a game and relate uncertainty with the value of the game. A new function called uncertain α-Coordination value is proposed to allocate public resources amongst vulnerable groups in an uncertain environment, a topic that has not been explored yet. The definitions of uncertain Shapley value with Choquet integral form and uncertain CIS value are proposed separately to establish uncertain α-Coordination value.