Endogenous strategic variable in a mixed duopoly

In this paper we endogenize the choice of strategic variables in a mixed duopoly market in which each firm produces a homogeneous product with a strictly increasing convex cost function. This allows us to endogenously determine the type of competition in a mixed duopoly. We get the interesting result that price competition is a dominant strategy for each firm in a mixed duopoly. The firms randomize among the prices belonging to the equilibrium range of price in Bertrand competition. It is different from the outcome in a simple duopoly market where both price competition and quantity competition are pure strategy Nash equilibrium. Thus, this paper establishes that the presence of a public firm influences the kind of competition that takes place in a duopoly market.