Abstract
This paper starts epistemic approaches of studying the Bayesian routing problem in the frame work of the network game introduced by Koutsoupias and Papadimitriou [LNCS 1563, pp.404–413. Springer (1999)]. It highlights the role of common-knowledge on the users’ individual conjectures on the others’ selections of channels in the network game. Especially two notions of equilibria are presented in the Bayesian extension of the network game; expected delay equilibrium and rational expectations equilibrium, such as each user minimizes own expectations of delay and social cost respectively. We show that the equilibria have the properties: If all users commonly know them, then the former equilibrium yields a Nash equilibrium in the based KP-model and the latter equilibrium yields a Nash equilibrium for social cost in the network game.
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Notes
- 1.
Mazalov [9], Chap. 9 pp.314–351.
- 2.
Example 9.6 in Mazalov [9] p. 324.
- 3.
Where \([\mathbf{l}_i = l]\) is defined by \([\mathbf{l}_i = l] = \{ \omega \in \varOmega \vert \mathbf{l}_i(\omega ) = l \}\). The last postulate BP means that ‘user i knows absolutely his/her selection of channel l.
- 4.
This is called the event-based approach in Fagin et al. [4].
- 5.
According to these properties we can say the structure \(\langle \varOmega , (K_{i})_{i \in N}\rangle \) is a model for the multi-modal logic S5n.
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Matsuhisa, T. (2016). Common-Knowledge and KP-Model. In: Nguyen, N.T., Trawiński, B., Fujita, H., Hong, TP. (eds) Intelligent Information and Database Systems. ACIIDS 2016. Lecture Notes in Computer Science(), vol 9621. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-49381-6_47
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