Summary: Bayesian Ignorance
May 9, 2010
We quantify the effect of Bayesian ignorance by comparing the social cost obtained in a
Bayesian game by agents with local views to the expected social cost of agents having global views.
Both benevolent agents, whose goal is to minimize the social cost, and selfish agents, aiming at
minimizing their own individual costs, are considered. When dealing with selfish agents, we
consider both best and worst equilibria outcomes. While our model is general, most of our results
concern the setting of network cost sharing (NCS) games. We provide tight asymptotic results
on the effect of Bayesian ignorance in directed and undirected NCS games with benevolent and
selfish agents. Among our findings we expose the counter-intuitive phenomenon that "ignorance
is bliss": Bayesian ignorance may substantially improve the social cost of selfish agents. We also
prove that public random bits can replace the knowledge of the common prior in attempt to bound
the effect of Bayesian ignorance in settings with benevolent agents. Together, our work initiates
the study of the effects of local vs. global views on the social cost of agents in Bayesian contexts.
Keywords: Bayesian games, local vs. global view, network cost sharing