Price leadership and firm size asymmetry: an experimental analysis

We use laboratory experiments to examine the effect of firm size asymmetry on the emergence of price leadership in a price-setting duopoly with capacity constraints. Independent of the level of size asymmetry, the unique subgame perfect equilibrium of our timing game predicts that the large firm is the price leader. Experimental data show that price leadership by the large firm is frequent, but simultaneous moves are also often observed. Profit outcomes in the previous period affect the subjects’ decisions to announce or wait in a way that hampers convergence to the equilibrium. Furthermore, while both small and large firms display a strong tendency to wait to announce their price when firm size asymmetry is low, they often set prices early when size asymmetry is high. Prices are higher when price setting is sequential rather than simultaneous and when firm size asymmetry is high. Hence, price leadership by either type of firm has an anti-competitive effect that is more pronounced when the size difference between firms is large.     

Cartels in the unidirectional Hotelling model

We study the impact of space on perfect collusion sustainability within the unidirectional Hotelling model where the firms are constrained to move to the left. We obtain that when the firm that located to the left of the Hotelling segment has the greater incentive to deviate, the distance between the firms has a negative impact on the capability of the firms to sustain the collusion in equilibrium. On the other hand, when the firm that located to the right has the greater incentive to deviate, greater spatial distance makes the collusion easier to sustain in equilibrium. These results substantially differ from the bidirectional Hotelling model.     

Optimal collusion under imperfect monitoring in multimarket contact

We investigate optimal collusion in repeated multimarket contact under imperfect public monitoring, where two firms operate in m markets and in each market, each firmʼs decision and public signals are binary. We show that in an optimal pure strategy strongly symmetric perfect public equilibrium, the size of efficiency loss is equal to that in the market with the most tempting deviation under single-market contact. Furthermore, we show a sufficient condition under which the symmetric equilibrium is optimal for joint payoff maximization among any perfect public equilibrium.     

Do cost efficiency gap and foreign competitors matter concerning optimal privatization policy at the free entry market?

In this paper, we demonstrate that in contrast to the case with exogenous number of foreign private firms, partial privatization is always the best policy for the public firm in long-run equilibrium, which casts doubt on the robust result in Matsumura and Kanda (J Econ 84(1):27–48, 2005) who argued that welfare-maximizing behavior by the public firm is always optimal in mixed markets. Critical cost gap determines that long-run degree of privatization is larger than the short-run one. In particular, regarding the scenario wherein one public firm competes with domestic private firms and foreign private firms, equilibrium price is lower than marginal cost of public firm instead of being equivalent to marginal cost of the public firm, and that public firm’s outputs, profit, and social welfare is the smallest in the concerned mixed oligopoly models.     

Vertical integration, raising rivals’ costs and upstream collusion

This paper analyzes the impact vertical integration has on upstream collusion when the price of the input is linear. As a first step, the paper derives the collusive equilibrium that requires the lowest discount factor in the infinitely repeated game when one firm is vertically integrated. It turns out this is the joint-profit maximum of the colluding firms. The discount factor needed to sustain this equilibrium is then shown to be unambiguously lower than the one needed for collusion in the separated industry. While the previous literature has found it difficult to reconcile raising-rivals’-costs strategies following a vertical merger with equilibrium behavior in the static game, they are subgame perfect in the repeated game studied here.     

Equilibrium Wage Dispersion,Firm Size,and Growth

This paper analyzes a model of equilibrium wage dynamics and wage dispersion across firms. It considers a labor market where firms set wages and workers use on-the-job search to look for better paid work. It analyzes a perfect equilibrium where each firm can change its wage paid at any time, and workers use optimal quit strategies. Firms trade off higher wages against a lower quit rate, and large firms (those with more employees) always pay higher wages than small firms. Non-steady-state dispersed price equilibria are also analyzed, which describe how wages vary as each firm and the industry as a whole grow over time. Journal of Economic Literature Classification Numbers: D43, J41.     

Market collusion and the politics of protection

This paper investigates the relationship between trade and competition policy within a model where market collusion and protectionist lobbying are themselves related. Collusion and lobbying are modeled as joint products of the same collective effort of firms. In equilibrium, firms cannot achieve greater cooperation in one dimension without reducing it in the other. A trade agreement that limits the effectiveness of lobbying may cause firms to increase market collusion, thereby increasing the domestic price. Thus, international trade agreements may run counter to the goals of competition policy. On the other side, a more restrictive competition policy is shown to either reduce the domestic price or reduce import protection. Thus, competition policy tends to promote trade policy goals. The reason is that restrictive competition policy undermines collusion at the source—it decreases the per-firm benefit to collusion relative to the gains from deviating—reducing firm cooperation in both dimensions.     

Debt as a collusive device in an oligopoly supergame

This paper explores the impact of debt holdings on the output decisions of firms in an oligopoly supergame with stochastic demand fluctuations. It is demonstrated that when perfect collusion is not feasible then there exist circumstances in which increased debt holdings may facilitate tacit collusion. This occurs because higher debt levels act as a credible commitment device which lowers the payoffs accruing to a firm when it defects from the tacitly collusive equilibrium. It is further shown that in these circumstances firms may have an incentive to hold debt for strategic purposes which promote collusion.     

QUANTITY VERSUS PRICE IN A HOMOGENEOUS PRODUCT DUOPOLY*

In a simple homogeneous product setting, the paper looks at the debate on whether firms should choose quantity or price as their strategic variable. It examines a two-stage game between firms with symmetric costs in which the firms choose the strategic mode of operation in the first period and then, in the second period, price or output are chosen simultaneously according to the mode chosen in the first stage. In this game it is possible to have two Nash equilibria where either both play in quantities or both play in prices. One firm choosing price and the other quantity can never be a Nash equilibrium in the two-stage game. Both choosing quantity is always a Nash equilibrium. Both choosing prices may be a Nash equilibrium only in some situations: the structure of the cost functions decides this issue.     

Price vs quantity in a duopoly supergame with Nash punishments

We examine the endogenous choice between price and quantity behaviour in a duopoly supergame with product differentiation. We find that (i) if cartel profits are evenly split between firms, then only symmetric equilibria s obtained; (i) if instead the additional profits available through collusion are split according to the Nash bargaining solution, there are parameter regions where all subgame perfect equilibria are asymmetric, with firms colluding in price–quantity supergames.     

Organizational Structure and the Choice of Price versus Quantity in a Mixed Duopoly

We consider the choice of price/quantity of a public and a private firm in a mixed differentiated duopoly. First, we study the way in which the strategic choice of the market variable is affected by different given organizational structures (managerial or entrepreneurial) of the public and the private firm. Second, we investigate how the price/quantity choice interacts with the endogenous choice of the organizational structure, thus determining a subgame perfect equilibrium at which firms choose to behave as price‐setters and to adopt a managerial structure.     

Price dispersion in a model of identical agents with perfect information

Abstract. The objective of this paper is to demonstrate that price dispersion is possible even in a world of perfect information and identical consumers and firms. The driving force in the model is service capacity and congestion cost. Each firm chooses a service capacity. Customers of a firm bear a congestion cost which, for a fixed service capacity, is an increasing function of the number of customers served by this firm. We demonstrate that under certain conditions the combined profit of two firms and the total surplus are higher in a price-dispersion equilibrium than in a single-price equilibrium.     

Keynesian unemployment as a nash equilibrium with endogenous wage/price setting: An example

A simple 3 good, 1 consumer, 1 firm model of fixed price, quantity constrained equilibrium is developed. A game is then defined on the set of (globally unique) equilibria. The consumer sets the money wage, the firm sets the money price of output (money is numeraire). Nash solutions of the game exist and may involve Keynesian unemployment but never involve Classical unemployment or Repressed inflation.     

COLLUSION,FLUCTUATING DEMAND,AND PRICE RIGIDITY*

We study an infinitely repeated Bertrand game in which an i.i.d. demand shock occurs in each period. Each firm receives a private signal about the demand shock at the beginning of each period. At the end of each period, all information but the private signals becomes public. We consider the optimal symmetric perfect public equilibrium (SPPE) mainly for patient firms. We show that price rigidity arises in the optimal SPPE if the accuracy of the private signals is low. We also study the implications of more firms and firms' impatience on collusive pricing.     

Product differentiation,price discrimination and collusion

The existing literature which analyses the relationship between the product differentiation degree and the sustainability of a collusive agreement on price assumes that firms cannot price discriminate, and concludes that there is a negative relationship between the product differentiation degree and the critical discount factor. This paper, in contrast, assumes that firms are able to price discriminate. Within the Hotelling framework, three different collusive schemes are studied: perfect collusion on discriminatory prices; perfect collusion on a uniform price; collusion not to discriminate. We obtain that the critical discount factor of the first and the third collusive scheme does not depend on the product differentiation degree, while the critical discount factor of the second collusive scheme depends positively on the product differentiation degree. Moreover, we show that imperfect collusion is more difficult to sustain than perfect collusion.     

The capital structure and investment of regulated firms under alternative regulatory regimes

This paper explains how regulated firms choose their capital structure and examines the effects of this choice on investment and on regulated prices. It is shown that in equilibrium, firms have an optimal debt level and that given this debt level, the regulated price is set high enough to ensure that firms never become financially distressed. The analysis of the equilibrium yields testable hypotheses concerning the effects of changes in cost parameters and in the regulatory climate on the equilibrium investment level, capital structure, and regulated price. The analysis also shows that a regulatory restriction on the ability of the firm to issue securities may have an adverse effect on investment and consequently may harm consumers.     

Profitability of price and quantity strategies in a duopoly with vertical product differentiation

Using a model according to Mussa and Rosen (1978) and Bonanno and Haworth (1998) we consider a sub-game perfect equilibrium of a two-stage game in a duopolistic industry in which the products of the firms are vertically differentiated. In the industry, there are a high quality firm and a low quality firm. In the first stage of the game, the firms choose their strategic variables, price or quantity. In the second stage, they determine the levels of their strategic variables. We will show that, under an assumption about distribution of consumers' preference, we obtain the result that is similar to Singh and Vives (1984)' proposition (their Proposition 3) in the case of substitutes with nonlinear demand functions. That is, in the first stage of the game, a quantity strategy dominates a price strategy for both firms. Received: April 23, 1999; revised version: May 31, 2000     

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     

CHOICE OF PRODUCT TYPE BY STRATEGICALLY INTERDEPENDENT FIRMS

The paper analyses the degree of product differentiation between sigle product firms in alternative market equilibria. The equilibria are stable in the sense of Nash, and both non-cooperative and tacitly collusive market outcomesare identified. The basic model follows the 'address' aproach to product differentiation, and the firms' strategic variables are choice of product type and price charged. When all firms are non-cooperative, product gaps between firms are equal; but tacit collusion results in product gap variation between firms in Nash equilibrium. In all cases, profits for any firm are assumed to be proportional to the multiple of the product gaps between that firm and each of its two closest rivals.     

CHOOSING ROLES IN A DUOPOLY FOR ENDOGENOUSLY DIFFERENTIATED PRODUCTS*

The choice of the roles by firms in a vertically differenitated duopoly is analysed introducing a preplay stage where firms set the timing of moves, under the alternative assumptions of full or non full market coverage. Under the first, it turns out that the unique subgame perfect equilibrium entails simultaneous play in the quality stage, followed by sequential play in the price stage, where both firms would prefer to be price leader, contrarily to the results obtained by previous literature. Under partial market coverage, it is possible to analyse both price and quantity competition. In such a case, simultaneous play in both stages emerges as the optimal behaviour. Overall, contrarily to the conclusions reached by the previous literature, it is not possible to claim that the choice of the strategy space dominates the distribution of roles.