Calculating explicit closed form solutions of Cournot models where firms have private
information about their costs is, in general, very cumbersome. Most authors
consider therefore linear demands and constant marginal costs. However, within this
framework, the nonnegativity constraint on prices (and quantities) has been ignored
or not properly dealt with and the correct calculation of all Bayesian Nash equilibria is
more complicated than expected. Moreover, multiple symmetric and interior Bayesian
equilibria may exist for an open set of parameters. The reason for this is that linear
demand is not really linear, since there is a kink at zero price: the general “linear”
inverse demand function is P(Q) = max{a − bQ, 0} rather than P(Q) = a − bQ.