  We address the question of whether price of stability results (existence of
equilibria with low social cost) are robust to incomplete information. We show
that this is the case in potential games, if the underlying algorithmic social
cost minimization problem admits a constant factor approximation algorithm via
strict cost-sharing schemes. Roughly, if the existence of an
$\alpha$-approximate equilibrium in the complete information setting was proven
via the potential method, then there also exists a $\alpha\cdot
\beta$-approximate Bayes-Nash equilibrium in the incomplete information
setting, where $\beta$ is the approximation factor of the strict-cost sharing
scheme algorithm. We apply our approach to Bayesian versions of the archetypal,
in the price of stability analysis, network design models and show the
existence of $O(\log(n))$-approximate Bayes-Nash equilibria in several games
whose complete information counterparts have been well-studied, such as
undirected network design games, multi-cast games and covering games.
