## Bayesian Nash Equilibrium in ``Linear'' Cournot Models with Private Information about Costs

**Sjaak Hurkens**

**Abstract:**
Calculating closed form solutions of general Cournot models where
firms have private information about costs is very cumbersome. Most
authors consider therefore linear demands and constant marginal
costs. However, within this framework, the nonnegativity constraint
on prices (and quantities) has not been 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 inverse demand is not really linear,
since there is a kink at zero price: *P(Q) = max {a-bQ,0 }* rather
than *P(Q) = a-bQ*.

**Keywords:** Cournot, Private Information, Bayesian
Nash
equilibrium.

**Classification Number:** C72, D43, D82.

International Journal of Economic Theory.
**10**: 203-217 (2014).