Asymmetric Oligopoly Research Articles

Bertrand‐Edgeworth game under oligopoly. General results and comparisons with duopoly

AbstractThis paper studies price competition among a given number of capacity‐constrained producers of a homogeneous commodity under the efficient rationing rule and constant (and identical) marginal cost until full capacity, when demand is a continuous, non‐increasing, and non‐negative function defined on the set of non‐negative prices and is positive, strictly decreasing, twice differentiable and (weakly) concave when positive. The focus is on general properties of equilibria in the region of the capacity space in which no pure strategy equilibria exist. We study how the properties that are known to hold for the duopoly are generalized to the oligopoly and we highlight the new properties that can arise in asymmetric oligopoly, which include the existence of an atom in the support of the equilibrium strategy of a firm smaller than the largest one, the properties that such an atom entails, the existence of gaps in the supports, and asymmetries in the equilibrium distributions of equally‐sized firms smaller than the largest one. Further, we provide results about the boundaries of the supports. Although the characterization of equilibria is far from being complete, this paper provides substantial elements in this direction.

Producing Green or Brown? A Game of Green Innovation in an Asymmetric Oligopoly

As consensus grows for low-carbon development, innovation becomes vital for green growth, given the substantial technology adoption needed for long-term environmental targets. This paper explores market-driven incentives for green product innovation in an asymmetric duopoly using a game theory approach without relying on direct government intervention. The roles that market dynamics and rivalry have on the supply of green or brown products are explored in simultaneous and sequential scenarios, considering technology costs, demand-creating effects, rivalry gains, and information availability. Results reveal that a fully green market is contingent on low innovation costs, depending especially on the magnitude of demand creation effects. Notably, product differentiation occurs only under extreme cost asymmetry. Recommendations underscore the importance of incentivising low-cost innovations, assessing the impact of product differentiation and diversity, especially concerning lower-income consumers, and proposing measures to improve the transparency of firms’ strategic choices.

Innovation and mergers in generalized asymmetric oligopolies

AbstractThis paper addresses the impact of horizontal mergers on innovation, in an industry with a generic number of low‐cost and high‐cost competitors who first decide their level of process innovation and then compete in quantities in the product market. We derive the Nash equilibrium expressions for this game as a function of all the parameters involved, including number of players of each type, production costs, cost reductions achieved, and associated process innovation costs. Model results and parameter dependency are then illustrated in with a simulation of horizontal merger effects.

The effects of optimal cross holding in an asymmetric oligopoly

AbstractThis paper studies the endogenous formation of cross holding and its welfare implications in an asymmetric Cournot oligopoly with one acquiring firm holding passive ownership in one of its rivals. With the presence of cost asymmetry, we show that the acquiring firm will always choose to hold ownership in the most efficient rival. The optimal level of ownership is determined by market demand, the number, and cost distribution of firms. We further analyze the welfare implications of cross holding and characterize both socially excessive and insufficient cross holdings.

Market shares and profits in two-sided markets

Using a logit demand model of asymmetric oligopoly in two-sided markets, I analyze the relationship between the market shares of platforms and their profits. In line with previous studies, I show that large market shares do not necessarily imply high profits. Decomposing a platform’s market shares on two sides of markets into the size (i.e., the sum of shares) and the structure (i.e., the ratio between shares), I find that, conditional on the size, profits are U-shaped in structure, and that, conditional on the structure, size is positively related to profits. This implies that the change in the structure on the two sides is critical to the understanding of the non-monotonic relationship between market shares and profits and that overall size can still be used as an indicator of the profitability of platforms as long as the structure is controlled.

Private versus public companies with strategic CSR

We analyze the effects of strategic Corporate Social Responsibility (CSR) on social welfare in an industry where firms are owned by consumers (publicly owned) and CSR commitment takes the form of a fraction of the consumer surplus into the firms’ objective function. We compare this market configuration with the standard case of firms owned by entrepreneurs (privately owned). In line with the empirical evidence, consumers’ ownership gives an incentive to adopt a socially responsible, welfare improving statute. While privately-owned companies are limited in the level of social concern to implement, publicly-owned companies are not, and CSR is welfare-improving for any level of social concern. Surprisingly, a market configuration of publicly-owned CSR companies decreases welfare compared to an oligopoly of privately-owned CSR companies. The analysis is then extended by considering asymmetric oligopolies with different company types.

Aggregative games and oligopoly theory: short‐run and long‐run analysis

AbstractWe compile an IO toolkit for aggregative games with positive and normative comparative statics results for asymmetric oligopoly in the short and long run. We characterize the class of aggregative Bertrand and Cournot oligopoly games, and the subset for which the aggregate is a summary statistic for consumer welfare. We close the model with a monopolistically competitive fringe for long‐run analysis. Remarkably, we show strong neutrality properties in the long run across a wide range of market structures. The results elucidate aggregative games as a unifying principle in the literature on merger analysis, privatization, Stackelberg leadership, and cost shocks.

Indirect taxation and undesirable competition

This paper studies undesirable competition in an asymmetric oligopoly under ad valorem taxation. We show that when the cost advantage of efficient firms is large, both the entry of and the cost reduction in efficient firms raise social welfare, but unexpectedly hurt consumers. Moreover, we find that unit taxation yields higher consumer surplus in equilibrium, and it could also be welfare superior to ad valorem taxation under certain conditions.

Endogenous Protectionism and Tariffication: Implications of the Interest Group Size and Free-Rider Problem

We endogenize bargaining power between the industry and the government to characterize an endogenous lobby formation and a general form of a protective import tariff in an asymmetric oligopoly. We show that the free-rider problem inevitably emerges in the market. The problem of free riding in the game, if serious, will lower the lobbying-endogenous tariff, with the rate subsequently approaching the welfare-maximizing level. Furthermore, an increase in the lobbying-endogenous tariff decreases social welfare in the game. Notably, welfare-improving trade liberalization occurs if the government removes the lobbying-endogenous tariff and moves toward free trade.

Flexible capacity strategy in an asymmetric oligopoly market with competition and demand uncertainty

AbstractThis article studies flexible capacity strategy (FCS) under oligopoly competition with uncertain demand. Each firm utilizes either the FCS or inflexible capacity strategy (IFCS). Flexible firms can postpone their productions until observing the actual demand, whereas inflexible firms cannot. We formulate a new asymmetrical oligopoly model for the problem, and obtain capacity and production decisions of the firms at Nash equilibrium. It is interesting to verify that cross‐group competition determines the capacity allocation between the two groups of firms, while intergroup competition determines the market share within each group. Moreover, we show that the two strategies coexist among firms only when cost differentiation is medium. Counterintuitively, flexible firms benefit from increasing production cost when the inflexible competition intensity is sufficiently high. This is because of retreat of inflexible firms, flexibility effect, and the corresponding high price. We identify conditions under which FCS is superior than IFCS. We also demonstrate that flexible firms benefit from increasing demand uncertainty. However, when demand variance is not very large, flexible firms may be disadvantaged. We further investigate the effects of cross‐group and intergroup competition on individual performance of the firms. We show that as flexible competition intensity increases, inflexible firms are mainly affected by the cross‐group competition first and then by the intergroup competition, whereas flexible firms are mainly affected by the intergroup competition. Finally, we examine endogenous flexibility and identify its three drivers: cost parameters, cross‐group competition, and intergroup competition. © 2017 Wiley Periodicals, Inc. Naval Research Logistics 64: 117–138, 2017

Market Concentration and Profitability of the Grocery Retailers in Central Europe

The aim of the article was to internationally compare the market concentration of grocery retailers in the six countries of Central Europe - Austria, Czech Republic, Germany, Hungary, Poland and Slovakia. The market concentration was measured by CR4 ratio, Herfindahl-Hirschman Index and the GRS index. Data covered the period 2010 - 2015. The secondary data came from the Euromonitor International and Bureau van Dijk databases. The results showed that the market structure of the Central European grocery retailers has mostly a character of asymmetric oligopoly. The pairwise correlation did not reveal any strong relationship between the market power and profitability of the grocery retailers. The Central European grocery market is controlled by strong national retail chains and multinational companies which operate modern grocery retail formats. However, traditional grocery retailers are still popular in Hungary while traditional individual grocers in other countries are disappearing or gradually joining the networking system based on franchising.

On the robustness and strategic implications of a parsimonious advertising – inventory competitive model with extensions to pricing competition

Using a market share attraction structure of advertising competition, this research introduces first, a parsimonious inventory-advertising model for which competition is limited to two symmetric firms thus obtaining its related comparative statics. Following a supermodular game approach, the derived comparative statics remain robust upon considering non-dominant firms (each with a market share of less than 50%) competing in an asymmetric oligopoly of N rivals where each firm controls the inventory/advertising decision variables. Furthermore, changes in model parameters are investigated in terms of their relative impact on equilibrium measures. In this regard, the findings indicate that for the analyzed model, the marketing parameters possess much more influence on the equilibrium measures than the operations parameters. The generalization appears applicable to both non-dominated oligopolies as well as dominated oligopolies (where one firm has a market share equal to or greater than 50%) where each firm controls the inventory/advertising decision variables in addition to price. However, changes in shift parameters elicit a response from the dominant firm which will differ from its non-dominant rivals for products and services. Additionally, while the literature shows that the non-dominant firm will pursue a defensive strategy of decreasing both the equilibrium price and the amount of equilibrium advertising in response to competitive entry, our findings show that results for a fixed market potential may not continue to be robust once inclusion of the operations variables of order quantity are considered. Finally, the study explores the implications of the free - entry equilibrium for which the number of firms in the industry is determined endogenously.

The Nonparametric Approach to Evolutionary Oligopoly

A recent paper of Carvajal, Deb, Fenske, and Quah (Econometrica 2013) applies the revealed preference approach in the context of a quantity competition oligopoly game. This paper aims to present a different solution concept for an evolutionary model in the asymmetric oligopoly setup where firms have diff erent cost functions to produce a homogenous good. Then, using the approach introduced by Carvajal et al. (2013), we derive the testable conditions of the evolutionary oligopoly model. Therefore, contrary to the typical empirical literature in IO, without making any parametric assumption regarding to the demand curve and the cost function, this nonparametric approach characterizes a set of conditions (restrictions) on observational dataset to be consistent with evolutionary oligopoly model. An empirical application to the oil market with OPEC producers and Non-OPEC producers is presented and we compare the rejection rates of both Cournot and evolutionary hypotheses.

Investment strategies in the Brazilian industry of aluminum cans: an analysis in the context of real options games

Objective – The purpose of this article is to analyze the impact of preemption (first move advantage, with the consequent emergence of negative externalities to competitors) in situations that consider the optimal moment for investment, in the context of asymmetric oligopolies, and using the options games method. Design/methodology/approach – The developed model was applied to the Brazilian aluminum can industry, in which three firms made up an asymmetric oligopoly, allowing strategic interactions and their consequences on firms’ investment decisions to be analyzed. Findings – In situations of preemption, the results show the relevance of using a dynamic model, allowing us to observe the importance of obtaining a competitive advantage in cost, and showing that it is possible to obtain monopoly profits or take advantage of isolated expansion for a longer period. If this advantage is great, rivals’ threat of preemption can be considered irrelevant, and that the firm will invest in monopolistic time, ignoring the possibility of rivals’ entry. Practical implications – In a competitive environment, firms need to decide whether the best strategy is to invest earlier, acquiring a competitive advantage over their rivals, or to postpone their investments, to acquire more information and mitigate the eventual consequences of market uncertainties. This work shows how to do it. Originality/value – This is the first paper that, by applying real options games, studies the impact of preemption of investment in the oligopolistic asymmetric environment of the Brazilian industry of aluminum cans.

Hamiltonian potential functions for differential games

We introduce the concept of Hamiltonian potential functions for noncooperative open-loop differential games and we characterise sufficient conditions for their existence. We identify a class of games admitting a Hamiltonian potential and illustrate the related properties of their dynamic structure. Then, we offer a preliminary exploration of the construction of potential functions for feedback games. As an illustration, we consider an asymmetric oligopoly game with process innovation.

Regulating termination charges in asymmetric oligopolies

This paper extends a standard Hotelling model to three firms and analyzes the competitive effect of asymmetric regulation on mobile and fixed termination charges. In the presence of fixed-mobile substitution, above-cost mobile termination charge creates a trade-off on the mobile network’s profit: i.e., (i) reducing retail profit by strengthening competition for subscribers (“price competition effect”), and (ii) raising termination profit by increasing market shares (“market share effect”). Our analysis shows that the competitive effect of asymmetric regulation on mobile and fixed termination charges is decided by the interaction between these two effects, which in turn depends on the distribution of customer types. That is, above-cost termination charges are likely to be beneficial to consumers for a sufficiently large fixed-mobile type (i.e., customers choosing between mobile and fixed networks) compared to a mobile type (i.e., customers choosing between mobile networks), while they are likely to be harmful to consumers for a small fixed-mobile type. It would be an important implication for regulatory authorities that there exist various factors to consider in regulating termination charges, including the industry development and market structure.

Evolutionary Stability in Asymmetric Oligopoly

It is a very well-known result that in terms of evolutionary stability the long-run outcome of a Cournot oligopoly market with fi nitely many fi rms approaches the perfectly competitive Walrasian market outcome (Vega-Redondo, 1997). However, in this paper we show that an asymmetric structure in the cost functions of fi rms may change the long-run outcome. Contrary to Tanaka (1999) we show that the evolutionarily stable price in an asymmetric Cournot oligopoly needs not equal the marginal cost, it may rather equal a weighted average of (diff erent) marginal cost. We apply a symmetrization technique in order to transform the game with asymmetric fi rms into a symmetric oligopoly game and then extend Schaff er’s defi nition (1988) of a fi nite population ESS (FPESS) to this setup. Moreover, we show that the FPESS in this game represents a stochastically stable state of an evolutionary process of imitation with experimentation.

Supply Function Auction for Linear Asymmetric Oligopoly: Equilibrium and Convergence

Abstract We study the supply function auction for an asymmetric oligopoly with uncertain linear demand function and linear marginal cost functions of producers. We examine existence of a supply function equilibrium (SFE) in the model and convergence of the best response dynamics to this equilibrium. We show that the dynamics converges to the SFE for a duopoly, but in general the SFE and the strong best response do not exist in the model.

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.

Strategic Investment Subsidies under Asymmetric Oligopoly

AbstractThis paper examines strategic investment subsidies in an international oligopoly. A general oligopoly model is constructed in which firms compete in two stages and governments commit to investment subsidies prior to firms' actions. The paper considers asymmetry among firms that arises from the nature of goods they produce rather than their cost structures. When firms produce asymmetrically differentiated goods, it is found that a change in the number of foreign competitors may alter the sign of the optimal unilateral investment subsidy. An example of policy reversal is provided in the case of strategic research and development subsidies for a quality‐differentiated industry.