Geodesic
Common-Knowledge and Bayesian Equilibrium in Network Game
Mathematica Applicanda, Tome 46 (2018) no. 2, pp. 211-243.

Voir la notice de l'article provenant de la source Annales Societatis Mathematicae Polonae Series

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.
DOI : 10.14708/ma.v46i2.6346
Classification : 91A40, 03B45, 90B10
Mots-clés : Bayesian routing game, Common-Knowledge, Conjecture, Expected delay equilibrium, Expected price of anarchy, Information partition, Nash equilibrium, Rational expectations equilibrium, Social costs 
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Takashi Matsuhisa. Common-Knowledge and Bayesian Equilibrium in Network Game. Mathematica Applicanda, Tome 46 (2018) no. 2, pp.  211-243. doi : 10.14708/ma.v46i2.6346. http://geodesic.mathdoc.fr/articles/10.14708/ma.v46i2.6346/

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