Asymmetric Firms Research Articles

On modeling the advertising-operations interface under asymmetric competition

Using a market share attraction structure of advertising competition and following a supermodular game approach, this article demonstrates for an asymmetric oligopoly, the directional impact of changes in model parameters on the marketing controlled variables of all rivals (advertising budgets) and the operations controlled variables of all rivals (ordered quantities). Importantly, the various changes are examined analytically, empirically and numerically in both non-dominated and dominated asymmetric oligopolies.In this regard, the results indicate that firms in a dominated oligopoly (one firm of market share larger than or equal to 50%) behave differently compared to firms in a non-dominated oligopoly (each firm of market share less than 50%) in response to changes in model parameters. Furthermore, changes in model parameters are investigated in terms of their relative influential impact on a variety of equilibrium measures. In this regard, the findings indicate that for the analyzed model the marketing parameters exert much more influence on the equilibrium measures than the operations parameters.Additionally, a change in the mode of competition from non-cooperation (oligopoly) to cooperation (joint ownership) dictates that strong asymmetric firms (of favorable marketing and operations parameters) continue advertising (but at lower levels) and weak asymmetric firms (of less favorable parameters) cease advertising altogether.

The Impact of Horizontal Merger and Acquisitions in Price Competition Models

The question of what impact mergers and acquisitions have on key equilibrium performance measures is fundamental to our understanding of competitive dynamics in an oligopolistic industry. We address these questions in the context of price competition models with differentiated goods and asymmetric firms allowing for general non-linear demand and cost functions merely assuming that both the pre- and post-merger competition games are super modular along with two minor technical conditions. We show that, in the absence of cost synergies, post-merger equilibrium prices exceed their pre-merger levels. Moreover, the post-merger equilibrium profit of the merged firms exceeds the aggregate of the pre-merger equilibrium profits of the merging firms. The equilibrium profit of the non-merging firms increases as well. We establish our results, at first, for settings where each firm in the industry offers a single product; we then generalize them to industries with multi-product firms. We also derive conditions under which cost synergies, by themselves, result in lower equilibrium prices than otherwise observed post-merger, and discuss how the combined effect of increased market concentration and cost synergies can be assessed efficiently.

The Weighted Set Covering Game: A Vaccine Pricing Model for Pediatric Immunization

The United States pediatric vaccine manufacturing market is analyzed using a static Bertrand oligopoly pricing model that characterizes oligopolistic interactions between asymmetric firms in a homogeneous multiple product market. Firms satisfy demand by appropriately pricing and selling its given set of bundles, where each bundle contains one or more products. In analyzing the pediatric vaccine market, a bundle is a vaccine, where each vaccine contains one or more immunogenic antigens. Consumers seek to purchase at least one of each antigen at an overall minimum cost. Demand is captured by defining a weighted set covering optimization problem, with the weights (prices) controlled by firms engaged in Bertrand competition. A repeated game version of the model enables multiple interactions between firms, allowing examination of tacit collusion. An iterative improvement algorithm is defined that constructs a pure strategy Nash equilibrium (some in the limiting sense) for the static game. Sufficient conditions for the existence of pure strategy Nash equilibria are provided, indicating that this class of games always yields at least one pure strategy equilibrium. Practical results of the pediatric vaccine market analysis follow from the difference in the repeated game equilibrium prices between two combination vaccines, Pediarix® and Pentacel®. Assuming the manufacturers of these vaccines agree to share the market equally with respect to volume, the equilibrium prices from the repeated game indicate a price difference of $0.86, whereas the difference in price between Pediarix® and Pentacel® for contract prices ending March 31, 2010 was $2.74. Interestingly, the subsequent public sector vaccine price list (contract prices ending March 31, 2011) shows a price difference of $0.95, with the price of Pentacel® actually reduced from the previous year—an unusual occurrence. The results presented in this paper suggest that a smaller price difference between these two important combination vaccines is appropriate, which is what occurred. In general, such results could serve to inform both manufacturers and purchasers on the appropriate pricing of combination vaccines, given the existence of a reasonable set of collusive agreements.

On a Nonrenewable Resource Extraction Game Played by Asymmetric Firms

A differential game of extraction of a nonrenewable resource is taken into account, where two firms compete over time and their two terminal times of extraction are two different random variables. The winning firm will be the only one remaining in the game after the first one retires. We explicitly compute the Hamilton---Jacobi---Bellman equations of the model and solve them in an asymmetric game with logarithmic payoff structure and linear state dynamics.

On the existence of supply function equilibria

Supply function equilibria are used in the analysis of divisible good auctions with a large number of identical objects to be sold or bought. An important example occurs in wholesale electricity markets. Despite the substantial literature on supply function equilibria the existence of a pure strategy Nash equilibria for a uniform price auction in asymmetric cases has not been established in a general setting. In this paper we prove the existence of a supply function equilibrium for a duopoly with asymmetric firms having convex non-decreasing marginal costs, with decreasing concave demand subject to an additive demand shock, provided that the second derivative of the demand function is small enough and not increasing. The proof is constructive and also gives insight into the structure of the equilibrium solutions.

Add-on Pricing by Asymmetric Firms

This paper uses an analytical model to examine the consequences of add-on pricing when firms are both horizontally and vertically differentiated and there is a segment of boundedly rational consumers who are unaware of the add-on fees at the time of initial purchase. We find that consumers who know the add-on fees can be penalized—and increasingly so—by the existence of boundedly rational consumers. Our consideration of quality asymmetries on base goods and add-ons, plus the inclusion of boundedly rational consumers, leads to several novel findings regarding firm profits. When quality asymmetry is on base goods only and with boundedly rational consumers, add-on pricing can diminish profit for a qualitatively superior firm and increase profit for an inferior firm (i.e., a lose–win result), compared to when add-on pricing is prohibited or infeasible. When quality asymmetries exist on both base goods and add-ons and without boundedly rational consumers, the opposite win–lose result prevails. When quality asymmetries exist on both base goods and add-ons and with boundedly rational consumers, the result can be win–win, win–lose, or lose–win, depending on the magnitude of quality differentiation on add-ons. This paper was accepted by J. Miguel Villas-Boas, marketing.

Unilateral Versus Coordinated Effects: Comparing the Impact on Consumer Welfare of Alternative Merger Outcomes

The nature of tacitly collusive behaviour often makes coordination unstable, and this may result in periods of breakdown, during which consumers benefit from reduced prices. This is allowed for by adding demand uncertainty to the Compte et al. (2002) model of tacit collusion amongst asymmetric firms. Breakdowns occur when a firm cannot exclude the possibility of a deviation by a rival. It is then possible that an outcome with collusive behaviour, subject to long/frequent break downs, can improve consumer welfare compared to an alternative with sustained unilateral conduct. This is illustrated by re-examining the Nestle/Perrier merger analyzed by Compte et al., but now also taking into account the potential for welfare losses arising from unilateral behaviour.

Judo economics in markets with asymmetric firms

I study a market entry game with price competition and perfectly substitutable products. Limiting the initial capacity (Judo economics) is a plausible entry strategy. I show that under asymmetry in production cost or product quality, capacity limitation can become obsolete.

Inefficient Entry Order in Preemption Games

In a preemption game, players decide when to take an irreversible action. Delaying the action exogenously increases payoffs, but there is an early mover advantage. Riordan (1992) shows that in a preemption game with two asymmetric players, players act in decreasing order of efficiency. This provides a microfoundation to the assumption that entry in a market occurs in the order of profitability, commonly used in the empirical analysis of market entry. We provide a counterexample showing that with more than two players this intuitive result can be reversed. We present a preemption game of entry into a new market. The potential entrants are three asymmetric firms: one efficient firm with high post-entry profits, and two inefficient firms. We show that the set of parameters such that the equilibrium entry order does not reflect the efficiency ranking is nonempty, and analyze which changes in post-entry profits preserve this entry order.

Inefficient entry order in preemption games

In a preemption game, players decide when to take an irreversible action. Delaying the action exogenously increases payoffs, but there is an early mover advantage. Riordan (1992) shows that in a preemption game with two asymmetric players, players act in decreasing order of efficiency. This provides a microfoundation to the assumption that entry in a market occurs in the order of profitability, commonly used in the empirical analysis of market entry. We provide a counterexample showing that with more than two players this intuitive result can be reversed. We present a preemption game of entry into a new market. The potential entrants are three asymmetric firms: one “efficient” firm with high post-entry profits, and two “inefficient firms”. We show that the set of parameters such that the equilibrium entry order does not reflect the efficiency ranking is nonempty, and analyse which changes in post-entry profits preserve this entry order.

WAGE BARGAINING AND MERGER INCENTIVES WITH ASYMMETRIC COSTS

ABSTRACTThis paper examines how wage bargaining within each firm influences the relationship between an equilibrium ownership structure and the most preferred ownership structure from the viewpoint of social welfare, in a unionized oligopoly of asymmetric firms with respect to productivity of capital. We consider the merger incentive of each firm’s owner when the wage level is determined through bargaining between the firm’s owner and union. We derive a condition for both the degree of cost asymmetry among existing firms and the relative bargaining power of each firm’s owner to her/his union such that each ownership structure can be observed in equilibrium. We also show that although the two types of ownership structures with the merger involving the least efficient firm can be equilibria and socially optimal, these structures are observed only when both the degree of cost asymmetry and the relative bargaining power of each firm’s owner are moderate. Finally, we analyse the relationship among the cooperative game approach employed in this paper and two non‐cooperative merger formation approaches, and examine the robustness of the results obtained in this paper against the change in the assumption regarding each firm’s cost function.

Entry Bias and Product Substitutability

The literature has established two kinds of entry bias in imperfectly competitive markets. First, free entry may lead to excessive entry relative to the socially optimal level. Second, free entry may lead to the wrong technology (type of firm) in the market compared to the socially optimal technology. This paper finds a product selection bias, a third kind of entry bias. We show that, in a Cournot market with asymmetric firms and imperfectly substituting goods, free entry may lead to fewer types of goods, more types of goods, or even a different type of good, compared to the social optimum.

Pricing online subscription services under competition

In recent times, rapid advances in the field of information technology have enabled firms selling information products (for example, in the form of a CD) to provide subscription services using remote servers. Making the product versus service decision involves a trade-off. Online subscription offerings are perceived to be of lower quality because of data security and network reliability issues but can reduce or even eliminate the credible commitment (of prices) problem typically faced by firms selling durable products. We model an infinite horizon game between two symmetric firms that choose the design architecture, that is, product or service (and consequent contracting scheme: selling or subscription) and then set prices to optimize profits. The perceived quality loss enables firms to differentiate based on design architecture/contracting scheme and make positive profits. Further, the firm that sells a product makes higher profit than the firm that offers a subscription service. However, as the discount factor increases, the presence of a seller leads to a credible commitment problem for both firms leading to a reduction in prices. The results offer an explanation for the persistence of firms selling products rather than services. Further, a firm offering a subscription service may be subject to price pressure due to the price commitment issues of a competing seller. We also extend our insights to other settings: one involving asymmetric firms and the other involving different discount rates for product quality and producer/consumer surplus.

Tax incidence under imperfect competition: Comment

Delipalla and O'Donnell (2001) contains a formula for the incidence of specific and ad valorem taxes in a conjectural variation oligopoly model with potentially asymmetric firms. The formula is incorrect. We derive the correct formula and provide a discussion of the error and its implications for empirical studies of pass-through.

A Note on Upward Pricing Pressure: The Possibility of False Positives

Farrell and Shapiro proposed a simple test of the possible upward pricing pressure (UPP) following a merger. They showed that the test may give false negatives, that is, indicate that a merger may not give an UPP, while a more comprehensive test would indicate the opposite. We show that their test applied to a case with asymmetric firms may give false positives.

Competitive and Harmonised R&D Policies for International R&D Alliances Involving Asymmetric Firms

We examine research and development (R&D) policies when a national firm forms an R&D alliance with a foreign competitor. Firms differ in their R&D capabilities, and adopt a profit-sharing rule when R&D decisions are coordinated. National R&D tax/subsidy policies are set independently or harmonized. When firms coordinate their R&D decisions and governments choose R&D policies independently, R&D taxes are chosen. But there is no intervention if policies are harmonized. These policy outcomes affect the types of R&D alliance choosen. Agreements to share R&D information may be preferred to those combining coordination of R&D decisions and information sharing because of the R&D tax that coordination attracts.

Irreversible Investment under Competition with a Markov Switching Regime

In this paper, we study an investment problem in which two asymmetric firms face competition and the regime characterizing economic conditions follows Markov switching. We derive the value functions and investment thresholds of a leader and a follower. One of the main results is that the equity risk premium in a recession regime is higher than that in a boom regime. The result theoretically supports the empirical finding in contrast to previous theoretical papers without regime switching.

Real Options Game Models of R&D Competition between Asymmetric Firms with Spillovers

Using real options game models, we consider the characterization of strategic equilibria associated with an asymmetric RD otherwise, sequential equilibrium would occur. When the initial hazard rate is low relative to the level of input spillover, simultaneous entry would occur as an optimal decision, signifying another scenario of dominant second mover advantage. On the other hand, when the initial hazard rate is sufficiently high so that the first mover advantage becomes more significant, simultaneous equilibrium does not occur even under high level of positive input spillover.

The Impact of Antitrust Fines on the Formation of Collusive Cartels

Abstract The literature on collusive cartels has mainly focused on the impact of antitrust fines on the sustainability of cartels, in infinitely repeated games. This approach, however, does not allow us to study the effect of antitrust fines on the incentives to form cartels in the first place. In this paper, we adopt a coalitional game approach to modeling collusive agreements, showing that antitrust fines may drive firms from partial cartels to a monopolistic cartel. Moreover, by introducing uncertainty on market demand, we show that the socially optimal competition policy can call for a finite or even zero antitrust penalty, even if there are no enforcement costs. We provide a sufficient condition for these results to apply to any coalitional game of cartel formation with symmetric firms. Then, we discuss the extension to asymmetric firms and dynamic collusion.

Tax Incidence Under Imperfect Competition

In a 2001 article that appeared in the International Journal of Industrial Organization, Delipalla and O’Donnell derive a formula for the incidence of an ad valorem or specific tax in a conjectural variations oligopoly model with potentially asymmetric firms (Delipalla and O’Donnell, 2001). However, the formula they derive is incorrect. We provide a brief discussion of their error and derive the correct formula.