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Communication and KP-Model

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Intelligent Information and Database Systems (ACIIDS 2017)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10192))

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Abstract

This paper treats a Bayesian routing problem from the epistemic point of view. We discuss on the role of communication among all users about the users’ individual conjectures on the others’ selections of channels in the network game. In this paper we focus on the expectations of social costs and its individual conjectures, and we show that, in a revision process of all users’ conjectures on the expectations of social costs by communication through the message on the conjecture among the all users, the process yields a Nash equilibrium for social cost in the based KP-model.

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Notes

  1. 1.

    See Fagin et al. [2].

  2. 2.

    Koutsoupias and Papadimitriou [5], Mazalov [7], Chap. 9, pp. 314–351.

  3. 3.

    \(\text {Supp}(\sigma _i)\) is defined by \(\text {Supp}(\sigma _i) = \{ l \in L\ \vert \ \sigma _i(l) \ne 0\}\).

  4. 4.

    Proposition 1 in Matsuhisa [6].

  5. 5.

    I.e., \(\text {Supp}(\mu ) = \varOmega \).

  6. 6.

    Where \([l]_i\) is defined by \([l]_i = [ \mathbf l _i = l] = \{ \omega \in \varOmega \vert \mathbf l _i(\omega ) = l \}\).

  7. 7.

    Theorem 1 in Matsuhisa [6].

  8. 8.

    There exists a time m such that for all t, \(\Pr (t) = \Pr (t+m)\). The period of the protocol is the minimal number of all m such that for every t, \(\Pr (t+m) = \Pr (t)\).

References

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Authors and Affiliations

  1. Ibaraki Christian University, Ohmika 6-11-1, Hitachi-shi, Ibaraki, 319-1295, Japan

    Takashi Matsuhisa

  2. Institute of Applied Mathematical Research, Karelia Research Centre, RAS, Pushkinskaya Ulitsa 11, Petrozavodsk, Karelia, 185910, Russia

    Takashi Matsuhisa

Authors
  1. Takashi Matsuhisa
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Correspondence to Takashi Matsuhisa .

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Editors and Affiliations

  1. Wrocław University of Science and Technology, Wroclaw, Poland

    Ngoc Thanh Nguyen

  2. Japan Advanced Institute of Science and Technology, Nomi, Japan

    Satoshi Tojo

  3. Japan Advanced Institute of Science and Technology, Nomi, Japan

    Le Minh Nguyen

  4. Wrocław University of Science and Technology, Wroclaw, Poland

    Bogdan Trawiński

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Matsuhisa, T. (2017). Communication and KP-Model. In: Nguyen, N., Tojo, S., Nguyen, L., Trawiński, B. (eds) Intelligent Information and Database Systems. ACIIDS 2017. Lecture Notes in Computer Science(), vol 10192. Springer, Cham. https://doi.org/10.1007/978-3-319-54430-4_68

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  • DOI: https://doi.org/10.1007/978-3-319-54430-4_68

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-54429-8

  • Online ISBN: 978-3-319-54430-4

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