We consider price regulation in oligopolistic markets when firms are quantity setters. We consider a market for a homogeneous good with a demand function of special form ( -linearity), constant returns to scale, and identical firms. Marginal costs can take two values only: low or high. Values of all parameters except the marginal costs are known to the regulator. Assuming that the regulator is risk-neutral and maximizes expected social welfare (defined as the sum of consumer surplus and profits), we characterize the optimal policy and show how this policy depends on the basic parameters of demand and costs. 1. Introduction One of the main causes of market failure is lack of competition. Thus, a completely informed and benevolent regulator should be able to find an allocation in which all agents are better off than under oligopolistic competition. A great deal of attention has been devoted to the case in which the regulator lacks sufficient information to implement efficient allocations and a single firm supplies the whole market (see the survey by [1] and the references therein). In contrast, the case of regulation under an oligopoly has been relatively neglected. All the papers we are aware of are generalizations of optimal regulatory schemes that were proposed for the case of a monopoly: Shaffer [2] and Kim and Chang [3] generalized the work of Loeb and Magat [4], Schwermer [5] and Lee [6] generalized the work of Sappington and Sibley [7], and López-Cu？at [8] generalized the work of Baron and Myerson [9]. In this paper, we investigate the performance of a particular mechanism, price regulation, under conditions of oligopolistic competition and compare the welfare properties under its implementation with those of oligopolistic competition, also referred to as the free market (Our model does not answer the question of the optimal mechanism. In fact, Bertrand competition among firms will attain first best results. So in our model, Bertrand competition cannot be enforced by the regulator. For instance, the regulator might enforce price competition among firms but if firms condition prices on outputs, the Cournot competition will result [10]. Another interpretation of our work is that we study the properties of a particular mechanism that has been used in reality). The motivation for our study is that price regulation is (or has been) used to regulate oligopolistic markets such as gasoline, natural gas, electric power generation, telecommunications, healthcare, pharmaceuticals, and so forth. Again, the initial work was done for the case of a regulated
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