Conjectural variation

Abstract: Conjectured supply function (CSF) models of competition among power generators on a linearized DC network are presented. As a detailed survey of the power market modeling literature shows, CSF models differ from previous approaches in that they represent each generation company's (GenCo) conjectures regarding how rival firms will adjust sales in response to price changes. The CSF approach is a more realistic and flexible framework for modeling imperfect competition than other models for three reasons. First, the models include as a special case the Cournot conjecture that rivals will not change production if prices change; thus, the CSF framework is more general. Second, Cournot models cannot be used when price elasticity of demand is zero, but the proposed models can. Third, unlike supply function equilibrium models, CSF equilibria can be calculated for large transmission networks. Existence and uniqueness properties for prices and profits are reported. An application shows how transmission limits and strategic interactions affect equilibrium prices under forced divestment of generation.

Abstract: The theory of oligopoly price is very sensitive to behavioral assumptions. Even given identical assumptions about costs and demand, different models can predict every price between marginal cost and monopoly. This paper selects a single oligopoly model, and thus predicts a single oligopoly price. The selection criterion is consistency of conjectures; each firm's conjectures about the way other firms react to it will be correct. The two classical oligopoly theories, Bertrand and Cournot, make identical assumptions about costs and demand, but different assumptions about firm behavior. In Cournot equilibrium, each firm maximizes profit given the quantity of output other firms produce. In Bertrand equilibrium, each firm maximizes given the prices other firms charge. This difference in behavioral assumptions leads to a large divergence in predicted prices. Cournot predicts positive markups that decline as the number of firms increases, while Bertrand predicts marginal cost pricing even in duopoly. Clearly both models cannot be correct. Is their truth an empirical question, as recent work suggests?' This paper attempts to decide on theoretical grounds. No attempt to decide among Bertrand, Cournot, and their more modern competitors can be based on mathematical correctness. Economic criteria must guide the decision. Oligopoly models are examples of what game theorists call Nash equilibrium. In them, every firm maximizes profits given the actions of all other firms. The mathematics does not care whether "actions" are defined to be prices (Bertrand), quantities (Cournot), or any other variables. Yet these distinctions are crucial to the economics of the situation. The notion of Nash equilibrium already entails one economic condition-individual rationality. This paper will determine the correct definition of actions by imposing a further economic conditionconsistency of conjectures.2 The precise sense in which conjectures are to be consistent is this; the conjectural variation and the reaction function will be equated. The conjectural variation is the firm's conjecture about other firms' behavior. In Cournot, for example, each firm conjectures that all other firms' quantities are constant. The reaction function is the firm's actual behavior. It is the solution to the profit-maximizing problem, and tells what the firm will do as a function of all other firms' actions. Clearly, what the firm conjectures affects how it reacts. This paper will search for cases where conjectures and reactions are the samewhere each firm's conjectures about other firms' reactions are perfectly correct, locally.3 Every notion of Nash equilibrium has the feature that, in equilibrium, each firm's beliefs about the level of all other firms' actions are confirmed. For example, in Cournot duopoly, each firm's equilibrium quantity is that one which induces the other firm to produce its equilibrium quantity. The firms are right in their beliefs, in Fellner's famous remark, but right for the wrong reason. That is, it is not actually true, as conjectured by the firm, that the other firm's quantity is a constant. The other firm's quantity depends nontrivially on ours-the reaction function does not have zero slope, although the conjecture does. This paper will find Nash equilibrium notions in which firms are right for

Abstract: This paper proposes an empirical methodology for studying various (implicit or explicit) collusive behaviors on two strategic variables, which are price and advertising, in a differentiated market dominated by a duopoly. In addition to Nash or Stackelberg behaviors, we consider collusion on both variables, collusion on one variable and competition on the other, etc. Using data on the Coca-Cola and Pepsi-Cola markets from 1968 to 1986, full information maximum likelihood estimation of cost and demand functions are obtained allowing for various collusive behaviors. The collusive hypothesis is not rejected, and the best form of collusive behavior is selected via nonnested testing procedures. Using the best model, Lerner indices are computed for both duopolists to provide summary measures of market power. Finally, our approach is contrasted with the conjectural variation approach and is shown to give superior results.