Fuzzy Harsanyi solutions for fuzzy level structure games with multi weight systems. (English) Zbl 1542.91053
Summary: In real life, the relationship between social or economic environment and resource constraints may impose restrictions on the formation of coalitions. More and more scholars have recognized the limitations of (crisp) cooperative games and propose fuzzy cooperative game models to better describe the partial cooperation between players. Based on this, we introduce level structure games under fuzzy coalition, and propose a new class of fuzzy values for these level structure games. We extend Harsanyi solutions to the fuzzy domain by linear fuzzy games and establish a general form of the Harsanyi solutions (FLH-value) for level structure games. In addition, we study two distribution systems based on FLH-value, which have absolute weight and relative weight respectively. The former satisfies the null player axiom, while the latter is not satisfied. The reason is that relative weight systems make weights of all priori coalitions change when building the characteristic function of every level, and a null player can obtain the excess profit from the overflowing Harsanyi dividend. Our research has certain implications for analyzing noncontributor distribution and maintaining alliance unity.
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