Price regulation in oligopoly

In this paper we consider price regulation in oligopolistic markets when firms are quantity setters. We consider a market for a homogeneous good with a special form of the demand function (ρ-linearity), constant returns to scale and identical firms. Marginal costs can take two values only: low or high. The regulator knows all parameters except marginal costs. Assuming that the regulator is risk neutral, we characterize the optimal policy and show how this policy depends on the basic parameter of demand and cost