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In this paper we investigate equilibriums in the Bayesian routing problem of the network game introduced by Koutsoupias and Papadimitriou [LNCS 1563, pp.404-413. Springer (1999)]. We treat epistemic conditions for Nash equilibrium of social cost function in the network game. 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 maximizes 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.Further the notion of price of anarchy is extended for rational expectations equilibriums in the models.
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2018
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2018-07-07
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bwmeta1.element.ojs-doi-10_14708_ma_v46i2_6346