Firm Scale and the Endogenous Timing of Entry: a Choice between Commitment and Flexibility

This paper presents a model of stochastic oligopoly with demand uncertainty where firms endogenously choose entry timing. We examine two extreme types of market structure and show that the equilibrium correspondence that connects them is continous. With two identically sized firms, there are symmetric, Cournot type equilibria where the probability of early entry declines with greater uncertainty, and for low uncertainty two asymmetric equilibria. With one large firm with a continuum of nonatomic firms, there is a unique Stackelberg equilibrium. We conclude that the behavior of a dominant firm with a finite fringe can be approximated by Stackelberg equilibrium.Journal of Economic LiteratureClassification Numbers?: D21, L11.     

Cournot and Stackelberg Duopolies Revisited

First, conditions are derived for a leader (or a follower) to be more advantageous than a follower (or a leader) in Stackelberg duopoly with symmetric firms and without product differentiation. Second, the equilibria in Cournot and Stackelberg duopolies are compared under a set of reasonable assumptions. If the reaction function slopes upward, the Cournot duopolists' profits turn out to be lower than those of both the Stackelberg leader and follower, and the equilibrium industry output is smaller in Stackelberg duopoly than in Cournot duopoly.
JEL Classification Numbers: D21, D43, L13.     

Stackelberg Beats Cournot — On Collusion and Efficiency in Experimental Markets

We report on an experiment designed to compare Stackelberg and Cournot duopoly markets with quantity competition. We implement both a random matching and a fixed-pairs version for each market. Stackelberg markets yield, regardless of the matching scheme, higher outputs than Cournot markets and, thus, higher efficiency. For Cournot markets, we replicate a pattern known from previous experiments. There is stable equilibrium play under random matching and partial collusion under fixed pairs. We also find, for Stackelberg markets, that competition becomes less intense when firms remain in pairs but we find considerable deviations from the subgame perfect equilibrium prediction which can be attributed to an aversion to disadvantageous inequality.     

A Two-stage Cournot Duopoly with Inventory Costs

This paper analyses the Cournot duopoly model which has two production periods before the market clears. As shown by Saloner (1987), if inventory costs are zero, many outcomes including both Cournot and Stackelberg outcomes are subgame perfect equilibrium outcomes. However, if small inventory costs are introduced, the Cournot outcome is no longer found in equilibrium and the equilibrium outcomes are only of Stackelberg-type. This suggests that more attention should be paid to the Stackelberg model than to the Cournot model.     

Learning to collude: An experiment in convergence and equilibrium selection in oligopoly

The paper considers a simple oligopoly model where firms know their own and the average pay-off in the industry. Firms choose decision rules for trading. The theory predicts that there are three types of Nash equilibria in this game (collusive, Cournot and Stackelberg). Our experiments test the selection process. We find that there is clear evidence of convergence to an equilibrium, and whilst both Cournot and collusive outcomes were selected, the collusive equilibrium is more common. The experimental results also give insights into the process of individual learning, confirming that subjects follow aspiration rules rather than reinforcement rules.     

MARKET PRICE MECHANISMS AND STACKELBERG GENERAL EQUILIBRIA: AN EXAMPLE

This paper considers Stackelberg competition in a general equilibrium framework with a productive sector. The working of market power and the configurations of strategic interactions are complexified by the presence of a leader. Two market price mechanisms are studied: one is associated with the Stackelberg–Walras equilibrium and the other is linked to the Stackelberg–Cournot equilibrium. Throughout the example of a two commodity economy, several results are obtained about equilibria mergings and about welfare comparisons.     

Nonlinear incentive provision in Walrasian markets: a Cournot convergence approach

The paper studies insurance with moral hazard in a system of contingent-claims markets. Insurance buyers are modelled as Cournot monopolists or oligopolists. The other agents condition their expectations on market prices, as in models of rational-expectations equilibrium with asymmetric information. Thereby they correctly anticipate accident probabilities corresponding to effort incentives induced by insurance buyers’ net trades. When there are many agents to share the insurance buyers’ risks, Cournot equilibrium outcomes are close to being second-best. In contrast, if insurance buyers are price takers, equilibria fail to exist or are bounded away from being second-best.     

Public Input Competition under Stackelberg Equilibrium: A Note

This paper examines the Stackelberg equilibrium for public input competition and compares it with the noncooperative Nash equilibrium. Given two asymmetric regions, we show that under the Nash equilibrium the more productive region tends to spend more on public input, which results in this region attracting more capital than the less productive region. The comparison of the two equilibria reveals that the leader region obtains a first‐mover advantage under the Stackelberg setting. This suggests that if regions interact with each other sequentially as in the Stackelberg equilibrium, then the regional disparity that is due to the heterogeneity of productivity is likely to be mitigated or enlarged, depending on which region performs the leadership role in the competition process.     

A Two-stage Price-setting Duopoly: Bertrand or Stackelberg

This paper investigates a two-stage price-setting duopoly with differentiated goods. First, each firm announces its price; second, it chooses its actual price; and finally the market opens. Once a firm announces a price, it is able to discount it but not raise it. The model includes Stackelberg-type and Bertrand-type equilibria as possible outcomes. Whether Bertrand or Stackelberg appears in equilibrium depends on the properties of demand functions crucially. We find three patterns of equilibrium outcomes; one case has Bertrand equilibrium only, another has Stackelberg only, and the other has both equilibria     

Instability in the implementation of Walrasian allocations

The existence of game forms which implement Walrasian allocations as Cournot (Nash) equilibrium outcomes is well known. However, if the equilibria are also required to be locally dynamically stable, at least for environments with unique Walrasian allocations, this paper shows that the requisite game forms do not exist. Our definition of a game form entails certain regularity conditions, and requires the Cournot equilibrium to be unique when the Walrasian equilibrium is unique. The main result is that for such a game form, there does not exist a continuous-time strategy adjustment process which ensures the local stability of Cournot equilibria throughout a certain class of environments having unique Walrasian equilibria. Each trader adjusts his strategy in response to his own characteristics and the observed current strategies of others; but the direction and magnitude of adjustments are not constrained by any behavioral assumptions. The definitions permit the inclusion of an artificial player, such as an auctioneer, so the well-known tatonnement instability emerges as a special case.     

Comparing Cournot and Bertrand equilibria in an asymmetric duopoly with product R&D

We compare the Cournot and Bertrand equilibria in an asymmetric duopoly with product R&D competition. If a firm’s marginal cost is lower than that of its rival, then this firm (its rival) is referred to as the more (less) efficient firm. Under each mode of competition, there are three types of equilibria: blockaded-entry, deterred-entry, and accommodated-entry. Moreover, the presence of R&D investment makes it harder for the less efficient firm to survive. Cournot competition entails a unique equilibrium, whereas Bertrand competition may yield two equilibria. It is harder for the less efficient firm to survive under Bertrand competition than under Cournot competition. Versus Cournot competition, Bertrand competition yields higher industry output, and it shifts production from the less efficient firm to the more efficient firm. This result, together with the known size effect, explains the following three findings. First, the more efficient firm has a normal output ranking, whereas the less efficient firm may demonstrate an output reversal. Second, the more efficient firm may demonstrate a R&D reversal, whereas the less efficient firm has a normal R&D ranking (its Cournot R&D effort exceeds its Bertrand R&D effort). Third, Bertrand competition is more welfare-efficient than Cournot competition.     

Playing Cournot although they shouldn’t

Summary. In this note, we experimentally investigate the extended game with action commitment in a Cournot duopoly with asymmetric cost. Risk dominance considerations allow to select a unique equilibrium in which the low-cost firm is the Stackelberg leader. The data, however, do not support the theory as simultaneous-move play is modal. Average output choices are in line with the Cournot equilibrium. This suggests that Cournot is a much more robust predictor for competition in markets than theory suggests.Received: 14 October 2002, Revised: 1 December 2003, JEL Classification Numbers: C72, C92, D43. Correspondence to: Hans-Theo Normann     

Endogenous Timing with Incomplete Information and with Observable Delay

This paper analyzes endogenous timing in a duopoly model with incomplete information. Firms announce the period in which they will move before choosing an action and are then committed to their choices. Endogenous Stackelberg equilibria, with either the informed or the uninformed firm as the Stackelberg leader, may emerge. For most parameters, the Cournot equilibrium in the first production period results endogenously. Journal of Economic Literature Classification Numbers: C72; C73; D82; L10.     

The Cournot-Bertrand profit differential: A reversal result in a differentiated duopoly with wage bargaining

This paper compares Cournot and Bertrand equilibria in a downstream differentiated duopoly in which the input price (wage) paid by each downstream firm is the outcome of a strategic bargain with its upstream supplier (labor union). We show that the standard result that Cournot equilibrium profits exceed those under Bertrand competition - when the differentiated duopoly game is played in imperfect substitutes - is reversible. Whether equilibrium profits are higher under Cournot or Bertrand competition is shown to depend upon the nature of the upstream agents’ preferences and on the distribution of bargaining power over the input price. We find that the standard result holds unless unions are both powerful and place considerable weight on the wage argument in their utility function.     

On the comparison of price and quantity competition under endogenous timing

This paper compares Bertrand and Cournot equilibria in a differentiated duopoly with linear demand, and asymmetric constant marginal cost under endogenous timing. It shows that endogenous timing leads to two sequential play with both leader–follower configurations in Bertrand, but simultaneous play in Cournot. Moreover, every firm’s mark-up/output ratio and the two firms’ weighted ‘average’ price are all lower, but the two firms’ weighted ‘average’ output is higher in either of the two sequential Bertrand equilibria than in the simultaneous-move Cournot equilibrium.     

Oligopoly with a large number of competitors: asymmetric limit result

We address how profitable innovation is in a competitive market by investigating the asymmetric oligopoly model in which 1 firm (innovator) has a cost advantage that is not drastic enough for her to become a monopolist, and by inducing asymmetric limit outcomes when the number of the other firms (laggard firms) goes to infinity. If the innovator is the Stackelberg leader, two cases can arise: (i) the innovator behaves as in the competitive market or (ii) she occupies the entire market but cannot make the price. If we consider Cournot competition, the innovator becomes the partial monopolist. An erratum to this article can be found at     

On the endogeneity of Cournot-Nash and Stackelberg equilibria: games of accumulation

We characterize equilibria of games with two properties: (i) Agents have the opportunity to adjust their strategic variable after their initial choices and before payoffs occur; but (ii) they can only add to their initial amounts. The equilibrium set consists of just the Cournot-Nash outcome, one or both Stackelberg outcomes, or a continuum of points including the Cournot-Nash outcome and one or both Stackelberg outcomes. A simple theorem that uses agents’ standard one-period reaction functions and the one-period Cournot-Nash and Stackelberg equilibria delineates the equilibrium set. Applications include contribution, oligopoly, and rent-seeking games.     

Non-renewable resource Stackelberg games

The market structure for many mineral industries can be described as oligopoly with potential for Stackelberg leadership. This paper derives and analyzes dynamically consistent extraction equilibria in a two-period discrete-time “Truly” Stackelberg (TS) model of non-renewable resource extraction, where firms move sequentially within each period and where both the leader and follower have market power. We show how the leader may be able to manipulate extraction patterns by exploiting resource constraints. Whether the leader wants to speed up its own production relative to the Cournot–Nash (CN) equilibrium depends on the shape of its iso-profit curve, which is affected by the two firms’ relative stock endowments and relative production costs. If the leader extracts faster, then the follower extracts slower, but in aggregate the industry extracts faster. Unlike static Stackelberg games, the follower does not necessarily have a second mover disadvantage.     

Multinational Corporations, Stackelberg Leadership, and Tariff-jumping

In this paper we consider the traditional entry mode choice of an incumbent monopolist facing entry by a single foreign firm. By allowing entry to be either via exporting or foreign direct investment and for the possibility of Stackelberg equilibria where firms can set quantities in one of two time periods, namely “early” or “late,” we find conditions where both Cournot and Stackelberg equilibria emerge endogenously. Furthermore, by introducing a simple linear tariff, we see that it not only affects the choice of exporting and FDI in a nonlinear way, but that it can also affect the type of equilibrium that emerges.     

On the role of network externalities in strategic delegation contracts with an industry-wide union

This article analyses the role of network externalities in managerial delegation contracts for differentiated products when the marginal product costs (the wage) are set by an industry-wide union. The results show that, in both Bertrand and Cournot equilibria, each owner offers a profit-oriented incentive scheme to his or her managers by penalizing sales maximization, irrespective of the strength of the network externalities. In the presence of weak network externalities and low product differentiation, firms can obtain higher profits in the equilibrium under Cournot-type quantity competition compared with that under Bertrand-type price competition. Furthermore, the wage chosen by the union is higher in the Cournot than in the Bertrand equilibrium. In the Cournot equilibrium, the wage increases with the strength of the network externalities. However, in the Bertrand equilibrium, there exists a threshold level of the degree of product differentiation.