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.     

Managerial incentives and collusive behavior

I characterize the effects of empirically observed managerial incentives on long-run oligopolistic competition. When managers have a preference for smooth time-paths of profits - as revealed by the empirical literature on “income smoothing” - manager-led firms can sustain collusive agreements at lower discount factors. Capped bonus plans and incumbency rents with termination threats make collusion supportable at any discount factor, independent of contracts' duration. When managers have these preferences/incentives and demand fluctuates, “price wars during booms” need not occur: the most collusive price may then be pro-cyclical.     

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.     

The critical discount factor as a measure for cartel stability?

This paper considers the stability of tacit collusion in price setting duopolies with repeated interaction. The minimum discount factor above which tacit collusion can be sustained in a subgame perfect equilibrium is called the critical discount factor δ*. In addition, δ* is often used as an intuitive measure for the stability of a tacit cartel, assuming that a collusive equilibrium is more difficult to sustain when δ* increases. However, according to standard theory the distance δ − δ* between the actual and the critical discount factor does not matter for stability as long as δ > δ*. This paper contributes experimental evidence that supports the intuitive idea that a larger critical discount factor makes collusion a less likely outcome.      

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.     

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.     

On the Relationship Between Innovation and Product Market Competition

This paper considers a theoretical model where firms reduce their initial unit costs by spending on R&D activities in a collusive market and where firms are able to coordinate on distinct output levels other than that of the unrestricted joint profit maximization outcome. We show that, in our model, the degree of collusion (captured by the discount factor) reduces the incentive to innovate when innovation is made non‐cooperatively. The reason is that non‐cooperative R&D introduces a negative externality where firms overinvest beyond the effort required to minimize the cost in order to extract profits from the rival firm, and a reduction in product competition helps internalize the externality. In a research joint venture the absence of R&D rivalry leads to contrary results. The main implication is that the validity of the Schumpeterian hypotheses depends on the extent of cooperation at the R&D stage.     

产品差别化、价格战与合谋

随着中国市场化改革的不断深入,价格战成为各行各业企业间不断上演的舞台剧。文章旨在从产品差别化与企业间合谋的相互关系出发,来分析企业频繁选择价格竞争而难以进行合谋的原因,即产品垂直差别水平的降低将使合谋难以维持,价格战容易爆发。因此,解决价格战的途径之一是中国企业应该加大自主创新的能力,提高产品垂直差别化程度。     

Endogenous rationing,price dispersion and collusion in capacity constrained supergames

This paper examines the feasibility of collusion in capacity constrained duopoly supergames. In each period firms simultaneously set a price–quantity pair specifying the price for the period and the maximum quantity the firm is willing to sell at this price. Under price–quantity competition firms are able to ration their output below capacity. For a wide range of capacity pairs, the equilibrium path providing the smaller firm with its highest stationary perfect equilibrium payoff requires that it undercut its rival’s price and ration demand. Furthermore, for some capacities and discount factors supporting security level punishments, price shading and rationing arise everywhere on the set of stationary perfect equilibrium paths yielding (constrained) Pareto optimal payoffs. That is, price shading may not only be consistent with optimal collusion, it may be a requirement of optimal collusion.     

Costly horizontal differentiation

We study the effect of quadratic differentiation costs in the Hotelling model of endogenous product differentiation. The equilibrium location choices are found to depend on the magnitude of the differentiation costs (relatively to the transportation costs supported by consumers). When the differentiation costs are low, there is maximum differentiation. When they are high, there is partial differentiation, with a degree of differentiation that decreases with the differentiation costs. In any case, the socially optimal degree of differentiation is always lower than the equilibrium level. We also study the case of collusion between firms. If firms can combine locations but not prices, they locate asymmetrically when differentiation costs are high and choose maximum differentiation when they are low. When collusion extends to price setting, there is partial differentiation.     

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.     

反垄断调查的一个鉴别：一致性定价行为背后的差异与合谋

如何区分成本上涨时企业同时涨价的行为究竟是价格合谋还是寡头竞争的企业正常的价格调整行为？这是反垄断执法机构面临的一个难题。本文通过数理模型证明了无论企业进行伯川德竞争还是古诺竞争，寡头竞争的企业的定价随着成本的变化存在一个连续调整路径，而组成卡特尔的企业的定价则会随着成本的变化出现一个不连续的跳跃。因此反垄断执法机构在观察到企业的一致性定价行为之后，如果能从以往的价格监测纪录中发现这些企业在成本下跌时，价格存在着更大幅度的下调，则可以据此怀疑这些企业存在着价格合谋，应开展更深入的调查来搜集这些企业违反《反垄断法》的全面证据。     

Collusive outcomes in price competition

In this paper we provide a sufficient condition for collusive outcomes in a single-shot game of simultaneous price choice in a homogeneous product market with symmetric firms and strictly convex costs. We also prove the counterintuitive result: if the second derivative of the cost function is nonincreasing in output, it is easier to sustain collusion when the number of firms increases.     

On prices’ cyclical behaviour in oligopolistic markets

We revisit the discussion about the relationship between price’s cyclical features, implicit collusion and the demand level in an oligopoly supergame where a positive shock may hit demand and disrupt collusion. The novel feature of our model consists in characterising the post-shock noncooperative price and comparing it against the cartel price played in the last period of the collusive path, to single out the conditions for procyclicality to arise both in the short and in the long-run. This poses an issue in terms of an antitrust agency’s ability to draw well defined conclusions on the firms’ behaviour after the occurrence of the shock, with particular reference for the litigation phase after a cartel breakdown.     

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.     

Entrepreneurial finance and economic growth

This paper develops a theory of the centralization of firms engaged in multi-market collusive agreements. A centralized organization (called the unitary or U-form) allows price coordination across several markets, whereas with decentralized (the multidivisional or M-form) firms the probability that the antitrust authority will find evidence of collusion on one market while investigating the other is lower. We show that the firm’s choice of internal structure depends to a large extent on product substitutability and the instruments used by the antitrust authority.     

Competition and the relative productivity of large and small firms

Using a comprehensive dataset on the incidence of price-fixing across British manufacturing industries in the 1950s, I compare collusive and competitive industries and find evidence of a negative relationship between collusion and the labour productivity of larger firms relative to smaller firms. In particular, collusion is associated with a reduction or even a reversal of the productivity gap between larger and smaller firms. This result is robust to controlling for the potential endogeneity of collusion.     

Price collusion with free entry: the parasitic competition

The market equilibrium that is generated in the presence of both price collusion and free entry is analyzed taking under consideration the case of a homogeneous product and the case of differentiated products. The outcomes of this market regime are compared with those of other regimes, including competition (or monopolistic competition), monopoly, fixed price with collusive entry limitation. Some welfare implications of the market regime of price collusion with free entry are examined, with respect to the maximum social welfare allocation and the allocations of other market regimes, so to highlight the inefficiency of price collusion with free entry. The number of producers results to be the maximum number of firms that can produce without incurring into losses. Therefore, social distress is caused by a displacement from the price collusion equilibrium with free entry. Its defence can thus be considered in reference to the desirability of social goals that are in contradiction with economic efficiency.     

Collusion and Price Rigidity

We consider an infinitely repeated Bertrand game, in which prices are publicly observed and each firm receives a privately observed, i.i.d. cost shock in each period. We focus on symmetric perfect public equilibria, wherein any "punishments" are borne equally by all firms. We identify a tradeoff that is associated with collusive pricing schemes in which the price to be charged by each firm is strictly increasing in its cost level: such "fully sorting" schemes offer efficiency benefits, as they ensure that the lowest-cost firm makes the current sale, but they also imply an informational cost (distorted pricing and/or equilibrium-path price wars), since a higher-cost firm must be deterred from mimicking a lower-cost firm by charging a lower price. A rigid-pricing scheme, where a firm's collusive price is independent of its current cost position, sacrifices efficiency benefits but also diminishes the informational cost. For a wide range of settings, the optimal symmetric collusive scheme requires (i) the absence of equilibrium-path price wars and (ii) a rigid price. If firms are sufficiently impatient, however, the rigid-pricing scheme cannot be enforced, and the collusive price of lower-cost firms may be distorted downward in order to diminish the incentive to cheat. When the model is modified to include i.i.d. public demand shocks, the downward pricing distortion that accompanies a firm's lower-cost realization may occur only when current demand is high.     

ON THE SUSTAINABILITY OF COLLUSION IN A DIFFERENTIATED OLIGOPOLY WITH A CARTEL AND A FRINGE

We discuss the effects of the existence of non‐colluding (fringe) firms on cartel sustainability. We obtain, using trigger strategies, that with product differentiation collusion is always more easily sustained when firms compete in prices than when firms compete in quantities. This is true basically because (i) price competition is more intense than quantity competition, and (ii) fringe firms exacerbate the fact that cartel firms have more incentives to deviate from the agreement under quantity competition. This result reverses previous findings where, in the absence of fringe firms, product differentiation plays a crucial role in determining the effectiveness of price or quantity competition in sustaining collusion.