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An Analog of the Bondareva–Shapley Theorem. II. Examples of \(V \)-Balanced Fuzzy Games

  • MATHEMATICAL GAME THEORY AND APPLICATIONS
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Abstract

This paper continues the research work [2], which generalizes the well-known Bondareva–Shapley theorem to the case of fuzzy cooperative \(n\)-player games. The conditions of \(V \)-balancedness are studied for three classes of fuzzy games as follows: 1) fuzzy transferable utility (TU) market games [3]; 2) fuzzy games associated with the linear-production models [6]; 3) fuzzy games generated by the rational distribution models of public costs during the construction of transport infrastructure facilities (the so-called airport games [5]). In addition to the conditions guaranteeing the non-emptiness of the cores, some types of non-dominated imputations of these games are also described. For the fuzzy airport games, such a description is exhaustive.

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Notes

  1. By analogy with standard games, a function \(v\) is redefined at the origin using the equality \(v(0) = 0\) .

REFERENCES

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Funding

This work was supported by the Russian Foundation for Basic Research, project no. 16-06-00101.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, 644043, Russia

    V. A. Vasil’ev

  2. Novosibirsk State University, Novosibirsk, 630090, Russia

    V. A. Vasil’ev

Authors
  1. V. A. Vasil’ev
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Correspondence to V. A. Vasil’ev.

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Vasil’ev, V.A. An Analog of the Bondareva–Shapley Theorem. II. Examples of \(V \)-Balanced Fuzzy Games. Autom Remote Control 82, 364–374 (2021). https://doi.org/10.1134/S0005117921020148

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  • DOI: https://doi.org/10.1134/S0005117921020148

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