Abstract
In this chapter we present another interesting model of games with a bilateral relation among the agents different to the communication model [6] (see Chap. 4) and the a priori unions one [7] (see Chap. 5). Hierarchical structures appears in a lot of human systems: firms, economic organizations, social networks, economic networks, protocolos... We consider several models in the literature with a same line which can be studied from bilateral relations. Gilles et al. [4] in 1992 introduced the conjunctive approach of permission structure.
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Notes
- 1.
The concept of hierarchy in van den Brink [8] for instance involves transitivity, reflexivity and also only one top in the structure.
- 2.
van den Brink [9] introduced another approach, the disjunctive one, for hierarchical permission structures. The fuzzy version of the model has been studied in Gallardo et al. [2] in the context of authorization structures (a broader field for hierarchical structures which are not necessarily bilateral relations).
- 3.
- 4.
- 5.
van den Brink [8] called this axiom weakly inessential player because he used another stronger version for the disjunctive approach.
- 6.
- 7.
Furthermore this option is not yet available in the literature.
- 8.
This axiom is not satisfied for all extension pl.
- 9.
This axiom is also not satisfied for any extension pl.
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Jiménez-Losada, A. (2017). Fuzzy Permission. In: Models for Cooperative Games with Fuzzy Relations among the Agents. Studies in Fuzziness and Soft Computing, vol 355. Springer, Cham. https://doi.org/10.1007/978-3-319-56472-2_6
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