Mixed Duopoly Research Articles

Efficiency comparison of unit and ad valorem taxation in mixed duopoly

In this paper, we consider the relative efficiency of unit taxation and ad valorem taxation in terms of welfare implications in different imperfectly competitive markets. Under the assumption that these two taxations can produce the same total output in equilibrium, which is also used by Anderson (2001), we show that ad valorem taxation is always welfare superior to unit taxation under full nationalisation, full privatisation, and partial privatisation.

Does Uniform Wage Decline the Welfare in a Budget-Constraint Mixed Market?

In this paper, we explore the influence of union structure and wage pricing strategies on the welfare under a mixed oligopoly which has a public firm with budget constraint. We showed that, the total utilities of the decentralized unions are higher than the utility of the centralized union under mixed duopoly if the centralized union charges a uniform wage and the productivity difference is large. The government should restrict the centralized union formed by the public and the private firm to charge discriminatory wages, and to avoid the improper use of the monopoly power of the labour union.

Strategic R&D risk choices of public and private firms

This paper investigates the R&D (research and development) risk choices of private and public firms in a product differentiated mixed duopoly market. Using the canonical models of R&D risk choice in a mixed market, it compares market performances between Cournot and Bertrand. The main findings are (i) public firm always engages in higher R&D risks than private firm under Cournot, (ii) public firm mostly chooses higher R&D risks, but may choose lower R&D risks than private firm if the degree of product substitution is sufficiently large under Bertrand, (iii) both public and private firms are more willing to take R&D risks under Bertrand than under Cournot, and (iv) from the perspective of social welfare, private firm always assumes too low R&D risks under Cournot. However, it takes excessive risks if the degree of product substitution is large enough under Bertrand.

Endogenous strategic variable in a mixed duopoly

In this paper we endogenize the choice of strategic variables in a mixed duopoly market in which each firm produces a homogeneous product with a strictly increasing convex cost function. This allows us to endogenously determine the type of competition in a mixed duopoly. We get the interesting result that price competition is a dominant strategy for each firm in a mixed duopoly. The firms randomize among the prices belonging to the equilibrium range of price in Bertrand competition. It is different from the outcome in a simple duopoly market where both price competition and quantity competition are pure strategy Nash equilibrium. Thus, this paper establishes that the presence of a public firm influences the kind of competition that takes place in a duopoly market.

Mixed duopoly and the indirect effect in linear supply function competition

The 1980s market reforms in Europe led to far-reaching privatization. However, empirical data show that some countries experienced deterioration in market performance, such as in consumer prices and welfare, during a certain period. Although theorists have focused on the change in the stock holding rate and the degree of product differentiation between privatization, few paid attention to the change in competition mode or intensity. To grasp how the structural change of privatization can affect market performance, we investigate the infinitesimal change in competition intensity by parameterizing it, apart from using the traditional method of making a simple comparison between Cournot and Bertrand equilibria. Thus, we parameterize the intensity of competition, and consider a mixed duopoly market with product differentiation accompanying partial privatization using a linear supply function approach. We observe a non-monotonic change in prices, profits, and social welfare in the plane of the degree of product differentiation and privatization, when competition becomes aggressive. Intuitively, when the semi-public firm promotes privatization, the market is an ordinary private duopoly and the competition becomes weak, while the competition can be aggressive with nationalization, since the semi-public firm tries to lower its price to improve consumer surplus. Further, the thresholds’ roughly common property—the right-upwardness—depends on the degree of the cross-price effect. Analytically, these counterintuitive phenomena are caused by the indirect effect inherent in linear supply function competition.

Combining the Endogenous Choice of the Timing of Setting the Levels of Strategic Contracts and Their Contents in a Managerial Mixed Duopoly

This study considers a game in which both, the timing of setting the levels of strategic contracts and their contents, are endogenized in a managerial mixed duopoly composed of a public firm with a welfare-maximizing owner and a private firm with a profit-maximizing owner. We suppose that the managers of both, the public firm and the private firm, adopt sales delegation contracts that are equal to the weighted sum of their profits and sales revenue with respect to the incentive parameters. We show that the market structure such that the manager of the public firm with a quantity contract is the follower and the manager of the private firm with a price contract is the leader can become the unique equilibrium market structure in the game in which both, the timing of setting the levels of strategic contracts and their contents, are endogenized in a managerial mixed duopoly. In addition, highest social welfare can be achieved in such a unique equilibrium market structure. Therefore, it is not necessary for the relevant authority, including the government, to regulate free decisions on the timing of the levels of the strategic contracts for the owners of both, the public firm and the private firm.

Combining the endogenous choice of the timing of setting incentive parameters and the contents of strategic contracts in a managerial mixed duopoly

This study considers a game in which both the timing of setting the incentive parameters and the contents of the strategic contracts are determined endogenously. We investigate this game in a managerial mixed duopoly comprising a public firm with a welfare-maximizing owner and a private firm with a profit-maximizing owner. We suppose that the managers of both firms are employed based on their sales delegation contracts, which are equal to the weighted sum of their profits and sales revenues with respect to their FJSV incentive parameters. We show that two equilibrium market structures are possible in this game: (1) the market structure in which the owner of the public firm is the follower with a quantity contract and the owner of the private firm is the leader with a price contract and (2) the market structure in which the owners of both firms use price contracts and set their FJSV incentive parameters simultaneously in the late period. Furthermore, we show that the highest degree of social welfare can be achieved with the first equilibrium market structure. Therefore, the game considered in this study differs from the game in which both the timing of setting the incentive parameters and the contents of the strategic contracts are determined endogenously in a managerial private duopoly composed of two firms with profit-maximizing owners. Specifically, in the game considered in this study, it is unnecessary for the corresponding authority, such as the government, to regulate the free determination of both the timing of setting the incentive parameters and the contents of the strategic contracts based on each firm's individual incentive. In addition, since the cost functions and their quantities are represented under the technologies of both firms, we confirm the results concerning the equilibrium market structures and welfare implications obtained in the case where both firms have constant marginal cost functions with respect to their quantities.

Privatisation and vertical integration under a mixed duopoly

This paper analyses the privatisation of public firms when private firms may be vertically integrated with their suppliers. We consider a mixed duopoly with a vertically integrated public firm. The private firm bargains the price of the input with its supplier if they are not vertically integrated. We find that for a given bargaining power of the private firm, it vertically integrates with its supplier if goods are weak substitutes. We also find that there is less vertical integration in the mixed duopoly than in the private duopoly. Finally, in general, the public firm is privatised when goods are close substitutes and the bargaining power of the private firm is low enough.

A Mixed Duopoly With Switching Costs

Abstract We examine the effects of switching costs in a two-period Hotelling-type model where a profit-maximising private firm competes with a welfare-maximising public firm. We show that, in contrast with the case in which both firms are private, where switching costs raise prices in both periods, in the mixed duopoly they raise prices in the second period but reduce them in the first period. Moreover, the first-period price reduction is of such magnitude that switching costs reduce firms’ profits and raise consumer welfare. We also find that switching costs affect the consequences of privatisation in favour of firms and against consumers.

Partial Privatization Policy and the R&D Risk Choice in a Mixed Duopoly Market

This study investigates how the partial privatization on the public firm affects the R&D risk choice in a mixed duopoly market. It mainly finds that: (i) the partial privatization of the public firm leads to a decline in the optimal level of R&D risk chosen by the private (or public) firm, and the higher the degree of privatization the lower the optimal level of R&D risk; (ii) for the public firm, the partial privatization policy always causes the private optimum to be lower than the social optimum; (iii) for the private firm, whether the private optimum is higher or lower than the social optimum depends on the partial privatization level of the public firm. When the degree of privatization is small (large), the private optimum is higher (lower) than the social optimum.

PRICE AND QUANTITY COMPETITION WITH ASYMMETRIC COSTS IN A MIXED DUOPOLY: A TECHNICAL NOTE

ABSTRACTWe consider a mixed duopoly in which private and public firms can choose to strategically set prices or quantities when the public firm is less efficient than the private firm. Thus, even with cost asymmetry, we obtain exactly the same result (i.e., Bertrand competition) of Matsumura and Ogawa (2012) if Singh and Vives’ (1984) assumption of positive primary outputs holds. However, compared to endogenous determination of the type of contract without cost asymmetry, our main finding is that in the wider range of cost asymmetry, different type(s) of equilibrium related to or not related to the limit‐pricing strategy of the private firm can be sustained. Thus, when considering an implication on privatization, we may overestimate the welfare gain of privatization because Cournot competition takes place after privatization even though cost asymmetry exists between firms. While the result of Matsumura and Ogawa (2012) holds true if the goods are complements, we find the novel results in the case of substitutes.

Dynamics and chaos control of a duopolistic Bertrand competitions under environmental taxes

This paper investigates the difference between price and quantity competition in a mixed duopoly game. We describe the behavior of a duopolistic Bertrand competition market with environmental taxes. There are two cases. In the first, the public firm is privatized and in the second, it is not privatized. In case I, private duopoly (postprivatization) where players use different production methods and choose their prices with (bounded rationality and naive). In case II, mixed duopoly (preprivatization) in this case there are two levels for the market including standard objective of the private firm is to maximize profits and including another objective function of the public firm namely “private welfare maximization”. We study numerically the dynamical behaviors of the models. The Nash equilibrium loses stability through a period-doubling bifurcation and the market in the end gets to be disordered. The disordered behavior of the market has been controlled by using feedback control method.

On supply function equilibria in a mixed duopoly

In this paper we present a mixed duopoly model of supply function competition under uncertainty with product differentiation. We find that, regardless the nature of product heterogeneity, the best response of the private firm always arises as strategic complement. Contrary to this, state-owned firm’s best response arises either as strategic complement or substitute depending on the product heterogeneity. As a result of the ex post realization of the demand uncertainty, different equilibria are reached.

Comparing welfare and profit in quantity and price competition within Stackelberg mixed duopolies

We compare welfare and profits under price and quantity competition in Stackelberg mixed duopolies. Under public leadership, price competition always yields greater profits and welfare than quantity competition. By contrast, under private leadership, the result depends on the nationality of the private firm. When the private firm is domestic (foreign), welfare is greater under quantity (price) competition. However, private firms always earn more under price competition. Introducing the nonnegative profit constraint affects welfare ranking but not profit ranking. These results indicate that profit ranking is fairly robust to the time structure in Stackelberg mixed duopolies, but welfare ranking is not.

A game theoretical approach to the effects of port objective orientation and service differentiation on port authorities' willingness to cooperate

This paper analyzes the effects of the objective orientation of port authorities and the level of service differentiation on the capacity, service price, profits and welfare among competing or cooperating ports. We also examine feasible combinations of these two factors (private objective level and service differentiation) to promote port co-operation. We apply the model starting from a mixed duopoly where a landlord port (a port authority with mixed public and private objectives) competes with a profit-seeking port (a port authority with a fully private objective) with differentiated services. The results show that both the private objective level of the port authority and the service differentiation level have a significant influence on various port competition and co-operation settings. Certain combinations of these factors prove to be useful in view of co-operation among port authorities which previously competed. The paper not only contributes to existing literature on port competition/co-operation and the use of game theory in a port setting. It also provides valuable inputs to port devolution and co-operation discussions at the policy level.

Complexity study on the Cournot-Bertrand mixed duopoly game model with market share preference.

In this paper, a Cournot-Bertrand duopoly model with market share preference is established. Assume that there is a degree of product difference between the two firms, where one firm takes the price as a decision variable and the other takes the quantity. Both firms are bounded rational, with linear cost functions and demand functions. The stability of the equilibrium points is analyzed, and the effects of some parameters (α, β, d and v1) on the model stability are studied. Basins of attraction are investigated and the evolution process is shown with the increase in the output adjustment speed. The simulation results show that instability will lead to the increase in the average utility of the firm that determines the quantity and reduce the average utility of the firm that determines price.

Duopoly models with a joint capacity constraint

This paper extends two recent models of duopoly with a joint capacity constraint (Nie and Chen in Econ Model 29:1715–1721, 2012; Nie in J Econ 112(3):283–294, 2014) by relaxing their crucial assumption that the game has an equilibrium which is unique and interior. Instead, this paper tackles a more basic issue on when their assumption applies. Our investigation is undertaken by using the best-response curve analysis. Both standard duopoly and mixed duopoly are considered, and both simultaneous moves and sequential moves are investigated. We find that their assumption applies only when the constraint is sufficiently weak, otherwise the equilibrium is either non-unique or corner.

Optimal Privatization and Subsidization Policies in a Mixed Duopoly: Relevance of a Cost Gap

This study considers subsidization and privatization policies in a mixed duopoly with one public firm and one private firm. The special feature of this study is that privatization can reduce the cost gap between the firms. We show that the optimal subsidy yields the efficient production allocation if privatization is not implemented. However, once the public firm is privatized, it overproduces under the optimal subsidy. Moreover, partial privatization is optimal unless privatization significantly reduces the cost gap.

Analysis of Two-Tier Healthcare Service Systems under Value-Based Competition in China

The Chinese tiered medical system falls far short in meeting the expectation that a patient visits a healthcare provider in community health services (CHS) institutions first, and, if necessary, gets the provider’s referral before seeing a specialist or going to a hospital. One of the most important reasons is the differential perceived value of patients on service quality. We model this issue as a two-tier service system and propose a solution to segment patients based on patient-perceived value for service quality. A mixed duopoly game is developed for analyzing the competition between CHS institutions and the hospitals, in which CHS institutions is to maximize its own total patients’ utilities, while the objective of the hospitals is to maximize its profit. Using game-theoretic analysis and queuing models to capture the operational performance of CHS institutions and the hospitals, we obtain the optimal strategies in equilibrium. This study generates managerial insights for practitioners to alleviate the burden of severe congestion in hospitals.

Product R&D Rivalry and Quality Policy in an International Industry Composed of Firms from Capitalist and Post-Communist Countries

Modeling an international mixed duopoly composed of a private firm from a capitalist country (CC), and a state firm from a post-communist country (PCC) that choose outputs and product qualities under quality policies of their governments, we analyze the firms’ output-quality rivalry and the governments’ quality policies. We find that when the PCC’s state firm is partially or perfectly privatized, an increase in the quality subsidy of each country raises its firm’s output, product quality and market share, but decreases those of its rival firm, and both the quality policies of the CC and PCC are the subsidy policies. However, when the PCC’s state firm is completely nationalized, while a change in the quality subsidy of the CC has the similar effects as those mentioned above, a change in the quality subsidy of the PCC has no effect on the firms’ outputs, product qualities and market shares, which means that the optimal quality policy of the CC is the subsidy policy, but that of the PCC is to do nothing.