Deriving profits allocation scheme in view of the players’ risk attitudes with interval-valued cooperative games

Abstract

Abstract Interval-valued cooperative games use interval numbers to represent the returns of coalition. It indicatives that the uncertain of the returns are emerge from the coalition. This leads to the uncertainty of the players’ returns who participating in the cooperation. The players with different risk preferences will have different attitudes towards the uncertainty of coalition returns. To address this issue, several allocation models are constructed by taking into account players’ risk attitudes. There are four types of players’ risk preference are concerned, namely, risk neutral, risk pursuit, risk aversion and risk mixed. First, to remove fuzziness of interval relationships presented in interval-valued core, the comparison method of interval numbers is utilized. Second, the allocation models are developed by taking into account decision makers’ risk attitudes and the absolute difference of two interval numbers, there are two types are concerned, that is, the allocation models respectively considering the coalition with the same satisfaction level of absolute difference and different satisfaction level of absolute difference. Third, an illustrative example is employed to demonstrate the validity and applicability of the proposed models. Finally, comparison of distribution schemes obtained in this study and obtained from other several methods are conducted.