Common-Knowledge and Bayesian Equilibrium in Network Game
Journal Title: Mathematica Applicanda. Annales Societatis Mathematicae Polonae Series III . - Year 2018, Vol 46, Issue 2
Abstract
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.
Authors and Affiliations
Takashi Matsuhisa
Keywords
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- EP ID EP653637
- DOI 10.14708/ma.v46i2.6346a
- Views 105
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