Common-Knowledge and Bayesian Equilibrium in Network Game

Takashi Matsuhisa

Common-Knowledge and Bayesian Equilibrium in Network Game

Takashi Matsuhisa

Mathematica Applicanda (2018)

Volume: 46, Issue: 2
ISSN: 1730-2668

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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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Takashi Matsuhisa. "Common-Knowledge and Bayesian Equilibrium in Network Game." Mathematica Applicanda 46.2 (2018): null. <http://eudml.org/doc/292724>.

@article{TakashiMatsuhisa2018,
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.},
author = {Takashi Matsuhisa},
journal = {Mathematica Applicanda},
keywords = {Bayesian routing game; Common-Knowledge; Conjecture, Expected delay equilibrium, Expected price of anarchy, Information partition, Nash equilibrium, Rational expectations equilibrium, Social costs},
language = {eng},
number = {2},
pages = {null},
title = {Common-Knowledge and Bayesian Equilibrium in Network Game},
url = {http://eudml.org/doc/292724},
volume = {46},
year = {2018},
}

TY - JOUR
AU - Takashi Matsuhisa
TI - Common-Knowledge and Bayesian Equilibrium in Network Game
JO - Mathematica Applicanda
PY - 2018
VL - 46
IS - 2
SP - null
AB - 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.
LA - eng
KW - Bayesian routing game; Common-Knowledge; Conjecture, Expected delay equilibrium, Expected price of anarchy, Information partition, Nash equilibrium, Rational expectations equilibrium, Social costs
UR - http://eudml.org/doc/292724
ER -

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