Geodesic
Two-stage minimum cost spanning tree game under fuzzy optimistic coalition
Contributions to game theory and management, Tome 15 (2022), pp. 81-95.

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This paper discusses the problem of cost allocation when players have different levels of optimism based on the two-stage minimum spanning tree game, and uses Choquet integral to calculate the characteristic function of fuzzy optimistic coalition and fuzzy pessimistic coalition. It is proved that the subgame of the two-stage clear optimistic coalition minimum cost spanning tree game is also a convex game. Finally, an example is used to prove that the two-stage fuzzy pessimistic coalition minimum cost spanning tree game has a dynamical instability solution.
Keywords: optimistic game, fuzzy game, Choquet integral, spanning tree game. 
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Zhao Guo; Dan Wang; Min Chen; Yin Li. Two-stage minimum cost spanning tree game under fuzzy optimistic coalition. Contributions to game theory and management, Tome 15 (2022), pp. 81-95. http://geodesic.mathdoc.fr/item/CGTM_2022_15_a7/

[1] Aubin, J., “Cooperative fuzzy games”, Mathematics of Operations Research, 6:1 (1981), 1–13 | DOI | MR | Zbl

[2] Bergantiños, G. and Vidal-Puga, J. J., “The optimistic TU game in minimum cost spanning tree problems”, International Journal of Game Theory, 36:2 (2007), 223–239 | DOI | MR | Zbl

[3] Bird, C. G., “On cost allocation for a spanning tree: A game theoretic approach”, Networks, 6:4 (1976), 335–350 | DOI | MR | Zbl

[4] Butnariu, D., “Stability and Shapley value for an n-person fuzzy game”, Fuzzy Sets and Systems, 4:1 (1980), 63–72 | DOI | MR | Zbl

[5] Cheng, M. and Li, Y., “New Characteristic Function for two-stage Games with Spanning Tree”, Contributions to Game Theory and Management, 14 (2021), 59–71 | DOI | MR

[6] Dianqing, Y. and Dengfeng, L., “Fuzzy coalition cooperative game method”, Fuzzy cooperative game method and its application, 2021, ed. Hao, J., Science Press, Beijing, 2021, 10, 27–59 (in Chinese)

[7] Dutta, B. and Kar, A., “Cost monotonicity, consistency and minimum cost spanning tree games”, Games and Economic Behavior, 48 (2004), 223–248 | DOI | MR | Zbl

[8] Kruskal, J. B., “On the Shortest Spanning Subtree of a Graph and the Traveling Salesman Problem”, Proceedings of the American Mathematical Society, 7 (1956), 48–50 | DOI | MR | Zbl

[9] Petrosyan, L. A. and Sedakov, A. A., “Two-Stage Network Games”, Vestnik of Saint Petersburg University. Series 10. Applied Mathematics. Computer Science. Control Processes, 4 (2014), 72–81

[10] Prim, R. C., “Shortest connection networks and some generalizations”, The Bell System Technical Journal, 36:6 (1957), 1389–1401 | DOI

[11] Shaohong, Y. and Macro, W., “fuzzy set”, Fundamentals and Applications of Fuzzy Mathematics, 2017, ed. Haiyan, Y., Chemical Industry Press, Beijing, 2017, 12, 8–41 (in Chinese)

[12] Tsurumi, M. Tanino, T. and Inuiguchi, M., “Theory and methodology: a Shapley function on a class of cooperative fuzzy games”, European Journal of Operational Research, 129:3 (2001), 596–618 | DOI | MR | Zbl

[13] Yin, L., “The dynamic Shapley Value in the game with spanning tree”, 2016 International Conference Stability and Oscillations of Nonlinear Control Systems, Pyatnitskiy's Conference, IEEE, 2016, 1–4