On the Core and Harsanyi Extensions of the Almost Positive Games Full article
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Optimization Problems of Complex Systems : International Asian School-Seminar 14-22 Aug 2023 , Новосибирск |
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| Source | 2023 19th International Asian School-Seminar on Optimization Problems of Complex Systems (OPCS) Compilation, IEEE. 2023. 6 c. ISBN 9798350331134. |
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| Output data | Year: 2023, Pages: 1-5 Pages count : 5 DOI: 10.1109/opcs59592.2023.10275764 | ||
| Tags | fuzzy cooperative game, fuzzy blocking, core, Shapley vector, Harsanyi extensions | ||
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| Affiliations |
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Funding (1)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0019 |
Abstract:
In the paper, we study interconnections between the cores and other solutions of the Harsanyi extensions of almost positive cooperative games. A short and elementary proof is given establishing that the cores of Aubin extensions of the games mentioned above consist of their Shapley values. The proposed approach is based on a generalization of the classical notion of a balanced cover in the theory of cooperative games on the case of fuzzy coalitions. This generalization allows us to expand the concept of a balanced ordinary cooperative game in situations where fuzzy blocking makes sense. In the preceding papers of the author it was shown that enlarging blocking capabilities by means of fuzzy coalitions doesn't prevent reasonable utilization of the linear programming methods (proved by O.N.Bondareva and L.S.Shapley to be very efficient in case of ordinary cooperative games). In particular, a criterion for the fuzzy game to have unblockable imputation turned out to be rather useful in clarifying some properties of Harsanyi extensions considered in the paper. One more example of the relevant application of the criterion mentioned is the main result of this work relating to the accessibility of core-imputations of the almost positive game via an appropriate fuzzy blocking. Here we take into account, as well, a close correlation between the cores and superdifferentials of fuzzy cooperative games, mentioned by J.-P.Aubin.
Cite:
Vasil'ev V.A.
On the Core and Harsanyi Extensions of the Almost Positive Games
In compilation 2023 19th International Asian School-Seminar on Optimization Problems of Complex Systems (OPCS). – IEEE., 2023. – C.1-5. – ISBN 9798350331134. DOI: 10.1109/opcs59592.2023.10275764 Scopus OpenAlex
On the Core and Harsanyi Extensions of the Almost Positive Games
In compilation 2023 19th International Asian School-Seminar on Optimization Problems of Complex Systems (OPCS). – IEEE., 2023. – C.1-5. – ISBN 9798350331134. DOI: 10.1109/opcs59592.2023.10275764 Scopus OpenAlex
Dates:
| Published print: | Oct 13, 2023 |
| Published online: | Oct 13, 2023 |
Identifiers:
| Scopus: | 2-s2.0-85175449933 |
| OpenAlex: | W4387620812 |