The research career of Paul Klemperer started with two articles with his Stanford supervisor Jeremy Bulow and Yale economist John Geanakoplos (see Bulow et al. 1985a, b).

The most revolutionary paper was the first: “Multimarket Oligopoly: Strategic Substitutes and Complements”. The idea of a strategic complement (substitute) is defined by the cross-partial derivative of the payoff function.

Why is the cross-partial derivative so important? Because the reaction func­tion is defined by the (necessary) standard first-order condition that the deriv­ative of the chosen action is zero. In the case of strategic complements, the reaction function will be upward sloping (as in the usual case of price compe­tition with differentiated products): in the case of strategic substitutes the reaction function will be downward sloping (as is typically the case in homo­geneous Cournot oligopoly). However, price competition can sometimes lead to strategic substitutes and quantity competition to strategic complements.

This very simple classification turned out to have a fundamental importance in terms of how oligopoly models behave—the paper applied the idea to a variety of settings. Its key insight led to the development of a whole literature on supermodular games, which generalised the notion of strategic comple­mentarity for payoff functions that were not twice continuously differentiable.

The other paper “Holding Idle Capacity to Deter Entry” applied the clas­sification of strategic complements and substitutes to Avinash Dixit's model of entry deterrence (see Dixit 1980). Dixit's model had assumed an incum­bent firm would always reduce output if a new firm was to enter, but Bulow et al.

Klemperer teamed up with his future wife Margaret Meyer^[225] (see Klemperer and Meyer 1986) to write a paper on the foundations of price versus quantity competition. Suppose that firms can choose whether to set price (and supply the quantity demanded) or choose quantity (and let the price be determined by the market). Furthermore, suppose there is a demand system linking the prices and outputs demanded of the firms. In the absence of uncertainty, firms are indifferent between setting a price or quantity. They face a demand curve and simply choose the profit maximising point on that curve (where marginal revenue equals marginal cost). The action of firm A does influence the demand curve for firm B, and hence firm B's best response. However, the best response can be attained by choosing either price or quantity. There are thus four types of (pure strategy Nash) equilibria with no uncertainty: the two firms both choose price, both choose quantity or one choses price and the other quantity. Bertrand and Cournot are both equilibria, as is the mixed price and quantity setting case. With demand uncertainty, matters are rather different. Firms will in general have a strict preference for setting price or quantity. The preference will depend on a variety of factors: the shape of the demand curve, the mar­ginal cost curve and the size of shocks. For example, a steep marginal cost curve makes quantity choice more attractive, and a flatter marginal cost curve favours price. If the model is symmetric, then the factors will influence both firms in the same way and tend to make the mixed equilibria less likely.

In two further papers, Klemperer and Meyer looked at equilibria in reac­tion functions (Klemperer and Meyer 1988) and supply functions (Klemperer and Meyer 1989). The 1988 paper, “Consistent Conjectures Equilibria: A Reformulation Showing Non-Uniqueness”, contributed to the literature on consistent conjectures which had been a topic rekindled by Timothy Bresnahan’s 1981 paper. Bresnahan was an Assistant Professor at Stanford in the period of Klemperer’s PhD. The conjectural variation (CV) acts to alter the first-order conditions for the optimal response and hence acts as a shift variable for the firm’s reaction function. By varying its CV, in effect a firm can move its reaction function. Firm A treats the reaction function of its competi­tor B as given: there will be a (unique) point on the other firm’s reaction func­tion that yields the highest profit for firm A. This point will be where there is a tangency between the iso-profit curve of firm A and firm B’s reaction func­tion. It can then choose its reaction function (via its CV) so that its own reac­tion function passes through this optimal point. Firm B can reason in the same way. What Klemperer and Meyer showed was that: (a) the equilibrium in reaction functions involves (Bresnahan) consistent conjectures (the conjec­tural variation equals the slope of the other firm’s reaction function); and (b) the equilibrium is highly non-unique in that almost any output pair corre­sponds to an equilibrium. The result rested on a geometrical intuition. If you pick any output pair, iso-profit curves of both firms pass through that point. The reaction functions that support this are the tangents to the iso-profit curves at that point. Neither firm can increase its profits by changing its reac­tion function given the other’s choice.

In the 1989 paper, “Supply Function Equilibria in Oligopoly Under Uncertainty”, Klemperer and Meyer revisited the issue of the strategic choice of whether to set a price or quantity.

2.1