Taxation and the sustainability of collusion: ad valorem versus specific taxes

Assuming constant marginal cost, it is shown that a switch from specific to ad valorem taxation that results in the same collusive price has no effect on the critical discount factor required to sustain collusion. This result is shown to hold for Cournot oligopoly when collusion is sustained with Nash-reversion strategies or optimal-punishment strategies. In a Cournot duopoly model with linear demand and quadratic costs, it is shown that the critical discount factor is lower with an ad valorem tax than with a specific tax that results in the same collusive price. However, in contrast to Colombo and Labrecciosa (J Public Econ 97:196–205, 2013) it is shown that the revenue is always higher with an ad valorem tax than with a specific tax.     

COLLUSIVE EQUILIBRIUM IN COURNOT OLIGOPOLIES WITH UNKNOWN COSTS*

The article studies collusive equilibria in an infinitely repeated Cournot oligopoly with unknown costs. I look at collusive pooled Perfect Bayesian equilibria and separating equilibria either with signaling or with communication. In the separating equilibria with signaling the firms play the strictly separating Bayesian Nash equilibrium in period 1 and produce the optimal incentive compatible collusive quantity vector from period 2 onwards. In the separating equilibrium with communication the optimal incentive compatible quantity vector is produced from period 1 onwards. Among these, the optimal separating equilibrium with communication gives the highest expected discounted joint profits.     

(Un)stable vertical collusive agreements

In this paper, we extend the concept of stability to vertical collusive agreements involving downstream and upstream firms, using a setup of successive Cournot oligopolies. We show that a stable vertical agreement, the unanimous vertical agreement involving all downstream and upstream firms, always exists. Thus, stable vertical collusive agreements exist even for market structures in which horizontal cartels would be unstable. We also show that there are economies for which the unanimous agreement is not the only stable one. Furthermore, the Stigler statement according to which the only ones who benefit from a collusive agreement are the outsiders need not be valid in vertical agreements.     

Optimal cartel trigger price strategies

A dynamical model of industry equilibrium is described in which a cartel deters deviations from collusive output levels by threatening to produce at Cournot quantities for a period of fixed duration whenever the market price falls below some trigger price. In this model firms can observe only their own production level and a common market price. The market demand curve is assumed to have a stochastic component, so that an unexpectedly low price may signal either deviations from collusive output levels or a “downward” demand shock.     

Individual best response in the repeated Cournot model

We propose a particular style of punishments to support collusive behavior in an infinitely repeated Cournot oligopoly model for at least the same range of discount factors as Friedman’s trigger strategies. The punishment lasts for a finite number of periods and asymmetry is introduced in such a way that each punisher’s output is the individual best response.      

Self-enforcing collusion in large dynamic markets

The “folk theorem” in game theory implies that any outcome that is better for all players than some single period Nash outcome can be achieved through noncooperative equilibrium in repeated games with discounting. Whether the folk theorem holds for a repeated Cournot oligopoly as the number of firms, N, increases without bound, is investigated. It is shown that the folk theorem holds in the limit iff demand increases at the same rate as the number of firms and the Cournot price sequence is bounded strictly above by the supremum of marginal cost for large N.     

Cartel sustainability with vertical product differentiation: Price versus quantity competition

In the context of a vertically differentiated duopoly, we analyse the influence of the degree of differentiation on cartel sustainability, under both price and quantity competition. We find that, under both Bertrand and Cournot competition, the effect of vertical product differentiation on sustainability of the collusive equilibrium is unclear. It is shown that, given a degree of differentiation, price collusion is more sustainable than quantity collusion.     

Coalition-proof supply function equilibria in oligopoly

In an industry where firms compete via supply functions, the set of equilibrium outcomes is large. If decreasing supply functions are ruled out, this set is reduced significantly, but remains large. Specifically, the set of prices that can be sustained by supply function equilibria is the interval between the competitive price and the Cournot price. In sharp contrast, when the number of firms is above a threshold we identify (e.g., three if demand is linear), only the Cournot outcome can be sustained by a coalition-proof supply function equilibrium.     

Is a Unique Cournot Equilibrium Locally Stable?

We consider a homogeneous product oligopoly, where the Cournot equilibrium is regular and unique. We show that for a duopoly, a unique Cournot equilibrium is always locally stable. For a “n” firm asymmetric cost oligopoly a unique Cournot equilibrium is locally stable under very general conditions. The sufficient conditions for local stability of a unique Cournot equilibrium are much less restrictive than what the existing literature suggests. For a symmetric cost oligopoly the unique Cournot equilibrium is almost always locally stable, except for a perverse case. Journal of Economic Literature Classification number: L13.     

The dynamics of some duopoly games involving the Market Share and Nichol strategies

The paper analyses the dynamics of some duopoly output games involving the Cournot, Market-Share and Nichol strategies. The model assumes linear price and cost functions and supposes that outputs are adjusted instantaneously at discrete time intervals. For all games considered, equilibrium is either reached after a finite number of moves or a stable approach to equilibrium occurs as t → ∞. In fact, apart from a few uninteresting cases, arising from the oversimplified form of the Market-Share strategy, all equilibrium points lie on specified parts of the firms' Cournot loci.     

Asymmetric rules for claims problems without homogeneity

We introduce a general class of rules for claims problems, called the difference rules, and demonstrate that a rule satisfies composition down and composition up if and only if it is a difference rule. We show that these rules are very simple to describe when there are two agents. In a variable population framework, we introduce a family of rules satisfying consistency, composition down, and composition up, which we term the logarithmic-proportional rules. These rules satisfy neither symmetry nor homogeneity.     

Two remarks on Cournot equilibria

We describe two simple results in the theory of Cournot equilibria. The first has to do with the effect of taxation in a Cournot industry and the second describes under what conditions a Cournot equilibrium will implicity maximize an objective function. These results are probably known, but are not well known, and they seem useful enough to be worth spelling out.     

Free entry and stability in a cournot model

In a Cournot model for a single homogeneous good, we study simultaneously two stability properties of a Cournot equilibrium: the stability of a continuous quantity adjustment process with a fixed number of firms and the stability relative to entry. Under usual assumptions, we show that these two properties are consistent—i.e., there exists an equilibrium that is stable in both senses—and determine quite sharply the number of active firms.     

Strategic interaction between futures and spot markets

We study an oligopolistic industry where firms are able to sell in a futures market at infinitely many moments prior to the spot market. A kind of Folk-theorem is established: any outcome between perfect competition and Cournot can be sustained in equilibrium. We then find that the Cournot outcome can be sustained by a renegotiation-proof equilibrium. However, this is not true for the competitive outcome. Furthermore, only the monopolistic outcome is renegotiation-proof if firms can buy and sell in the futures market. These results suggest, contrary to existing literature, that the introduction of futures markets may have an anti-competitive effect.     

Sustaining Collusion under Economic Integration*

In this paper, we aim at investigating from a game‐theory perspective whether trade liberalization can promote a collusive two‐way trade. We show that, under Cournot competition, economic integration is anti‐competitive if collusive trade is a possible outcome of the repeated game; under price competition, the likelihood of collusive trade is a necessary but not sufficient condition for trade liberalization to be pro‐competitive. Furthermore, we show that economic integration may increase the scope for collusion irrespective of the firms’ strategic variable.     

Dynamic efficiency of Cournot and Bertrand competition: input versus output spillovers

We consider the efficiency of Cournot and Bertrand equilibria in a duopoly with substitutable goods where firms invest in process R&D that generates input spillovers. Under Cournot competition firms always invest more in R&D than under Bertrand competition. More importantly, Cournot competition yields lower prices than Bertrand competition when the R&D production process is efficient, when spillovers are substantial, and when goods are not too differentiated. The range of cases for which total surplus under Cournot competition exceeds that under Bertrand competition is even larger as competition over quantities always yields the largest producers’ surplus.     

Bertrand versus Cournot revisited

Summary. Bertrand criticized Cournot's analysis of the competitive process, arguing that firms should be seen as playing a strategy of setting price below competitors' prices (henceforth, the Bertrand strategy) instead of a strategy of accepting the price needed to sell an optimal quantity (the Cournot strategy). We characterize Nash equilibria in a generalized model in which firms choose among Cournot and Bertrand strategies. Best responses always exist in this model. For the duopoly case, we show that iterated best responses converge under mild assumptions on initial states either to Cournot equilibrium or to an equilibrium in which only one firm plays the Bertrand strategy with price equal to marginal cost and that firm has zero sales. Received: December 11, 1995; revised version October 2, 1996     

Effect of credible quality investment with Bertrand and Cournot competition

We show how credible revelation and ability to commit to quality choice effect equilibrium qualities and welfare when product market is either Bertrand or Cournot competition. We show that results depend on the type of competition but not generally on the cost of quality function. We show that with Bertrand competition, the equilibrium qualities are lower with credible commitment. Competition is moderated and producer surplus is higher and consumer surplus lower. With Cournot competition, higher quality will be better but lower quality will be worse with credible commitment. Consumer surplus is always greater with credible commitment and if cost does not increase too quickly with quality, producer surplus will also increase. Thus credible commitment is a collusive device with Bertrand competition but it can improve social welfare with Cournot competition. Received: February 8, 2000; revised version: February 14, 2002 RID="*" ID="*" The idea of this paper originated in the weekly workshops of Mordecai Kurz at Stanford. I am forever in debted to Mordecai and fellow students – Luis Cabral, Peter DeMarzo, John Hillas, Michihiro Kandori, Steve Langois, Patrick McAllister, Steve Sharpe, Peter Streufert, Steve Turnbull and Gyu-Ho Wang – for their criticism and encouragement. I also benefited from comments from Yi-Heng Chen, Jin-Li Hu, Kala Krishna, Jinji Naoto, Thomas J. Prusa, and Shyh-Fang Ueng at various later stages of this work. Last but not least, I am grateful for the detailed comments of the referee.     

INTERTEMPORAL COURNOT AND WALRAS EQUILIBRIA: AN ILLUSTRATION*

In an intertemporal general equilibrium framework, we compare a Cournot equilibrium to the Walras equilibrium. The Cournot agents trade and invest less than the Walras agents. This generates an inefficiency that does not vanish as the number of Cournot agents tends to infinity. A larger number of strategic Cournot agents implies that the amount of trade (relative to their aggregate consumption) increases (i.e., it moves towards the Walrasian amount), but their investment (relative to the stock) decreases (i.e., it moves away from the Walrasian amount). "S'il y avait 3, 4, ...n producteurs en concurrence [...] la valeur de p, qui en résulte, diminuerait indéfiniment par l'accroissement indéfini du nombre n,”A. A. Cournot (1838, p. 63)."     

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