Environmental taxes in a differentiated mixed duopoly

Beladi and Chao (2006) and Bárcena-Ruiz and Garzón (2006) considered the role of environmental policy on the decision whether to privatize a public firm in different market structures. This paper re-examines whether privatization improves (or deteriorates) the environment in a mixed duopolistic framework with differentiated product and pollution abatement. It is shown that, due to privatization, less attention is paid to pollution abatement by all the firms coupled with less environment taxes levied by the government in a differentiated duopoly, and the environment is more (less) damaged when the product is less (more) substitutable. When the product is highly substitutable, industry profits increase because this softens the intensity of the product market, but social welfare deteriorates accompanied with the path of privatization because the loss of consumer surplus and tax revenue exceeds the increases in profits, even if the environment is less damaged.     

Endogenous managerial incentive contracts in a differentiated duopoly,with and without commitment

In a differentiated Cournot duopoly, we examine the contracts that firms' owners use to compensate their managers and the resulting output levels, profits and social welfare. If products are either sufficiently differentiated or sufficiently close substitutes, owners use Relative Performance contracts. For intermediate levels of product substitutability, they use Market Share contracts. When owners do not commit over the types of contracts, each type is an owner's best response to his rival's choice. Product substitutability has differential effects on output levels and profits, depending on the configuration of contracts in the industry. Finally, managerial incentive contracts are welfare enhancing if they increase consumers' surplus. Copyright © 2010 John Wiley & Sons, Ltd.     

Quality-improving R&D and merger policy in a differentiated duopoly: Cournot and Bertrand equilibria

We combine a model of product research and development (R&D) and technological spillover with the concept of technological distance and examine horizontal mergers in a duopolistic market with R&D. The results are fourfold. First, a merger can better encourage R&D investment than the competition case. Second, with a small degree of product differentiation (PD), the merger criterion under the Cournot duopoly is stricter than that of the Bertrand case. By contrast, with a moderate or large degree of PD, the opposite is true. Third, with a small technological distance, a merger should be allowable. Finally, with a small degree of PD and moderate technological distance, a merger should be allowable.     

Strategic pricing of differentiated consumer durables in a dynamic duopoly: A numerical analysis

Under different modes of competitive pricing behavior, profit-maximizing price trajectories are derived for durable products in a dynamic duopoly. Open-loop co-operative and non-cooperative pricing behavior is analyzed within a comprehensive model where sales of differentiated products are described by interlocked diffusion processes with realistic demand characteristics. Because of analytic complexity, the optimal trajectories implied by the control and differential-game problems are derived numerically across an extensive set of plausible market scenarios. Manipulation of initial market conditions enables derivation of optimal competitive pricing as a function of timing of entry.     

Asymmetric outcome in a symmetric dynamic duopoly

In a dynamic duopoly, will an initial asymmetry between firms increase or decrease over time? We examine this issue within a stochastic dynamic alternate-move duopoly model that explicitly accounts for action and reaction between firms. We consider two firms that are symmetric with regard to all primitives such as demand, cost and production functions, and which are subject to the same stochastic environment. The only asymmetry is with regard to their initial capital stocks which in turn asymmetrically influences their current and future profit and investment possibilities. We offer a characterization of the stochastic steady state and its supporting ergodic set for each firm. We are then able to identify the precise restrictions on the initial conditions under which the two firms either converge or diverge in the long run.     

Endogenous spillovers in a non-tournament R&D duopoly under uncertainty

Including R&D risk, this paper considers the choices of R&D spillovers in a simple non-tournament cost-reducing R&D duopoly game with Bertrand competition. It turns out that the two firms never disclose any of their R&D information when considering their R&D non-cooperatively. However, if the firms decide their R&D cooperatively, we show, though they would always fully share their information when the risk of R&D is low, they would not disclose any of their R&D information when the market competition is fierce, the R&D risk is high and the R&D is efficient.     

A differential game in a duopoly with instantaneous incentives

In this paper, we study a differential game in which two competing firms exploit a public renewable resource that is relevant from a landscape point of view. We consider a policy maker that provides an instantaneous incentive to the firms in order to prevent the resource exhaustion during the whole extraction period, which coincides with the harvesting license period. We compute an open-loop Nash equilibrium of the differential game, showing that it coincides with a linear feedback Nash equilibrium. Finally, we compute the value of the incentive that leads to the maximization of social welfare considering the incentive both as a pure transfer and as a cost.     

Environmental R&D and privatization in a mixed duopoly market

The study examines strategic environmental research and development (ER&D) under environmental tax in a mixed duopoly and further analyzes the impact of privatization on it. We show that the environmental tax may not necessarily promote the private (or public) firm's ER&D, and the relative ER&D performance between firms depends on the public firm's environmental attitudes and the tax rate. When the public firm cares much for environment, it can be used as an instrument to correct the private firm's underinvestment (or overinvestment) in ER&D. Moreover, privatization can (cannot) raise both firms' ER&D simultaneously if the tax rate is high (low).     

Endogenous timing of managerial delegation contracts in a unionized duopoly

In a multiple‐stage duopoly game with strategic delegation and unionized labor market, this paper analyzes whether firms' owners decide managerial incentive contracts sequentially or simultaneously. When firms compete in quantities, firms' owners can choose incentive contracts simultaneously or sequentially, depending on the unions' relative bargaining power and the degree of product differentiation. Instead, when firms compete in prices, firms' owners set incentive contracts sequentially with substitute goods and simultaneously with complement goods.     

Innovation subsidy under duopoly

Innovation plays extremely important roles in the society, and underinvestment in innovation popularly exists. This article aims to capture innovative subsidy with game theory model. First, unilateral subsidy stimulates both innovation and outputs of subsidized firms, while it deters those of opponents. Second, under innovation subsidy, relationship between subsidized firm's innovation and product substitutability satisfies a U shape. For opponents, it is also a U-shaped relationship. Third, under unilateral subsidy, subsidizing high-efficiency firms yields more innovation than subsidizing low-efficiency firms. Finally, bilateral subsidy stimulates more innovation than unilateral subsidy. This study supports theory to subsidize innovation efficiently.     

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.     

Strategic management under duopoly

The purpose of this paper is to present a general conjectural variation model to provide an integrative treatment of strategic management under duopoly. It is shown that the nature of the desired distortion of managers' incentives depends critically on the magnitudes of the managers' conjectural variations with respect to outputs as well as the owners' conjectural variations with respect to incentives. In particular, it has been demonstrated that when the owners' conjectural variations with respect to incentives are zero, the owners will motivate their managers to maximize profits and provide no incentives for sales under consistent conjectures. However, the owners make their managers behave more (less) aggressively and produce more (less) than profit-maximizers if the managers' conjectural variations with respect to outputs are larger (smaller) than the actual response.     

Irreversible investment and R&D spillovers in a dynamic duopoly

Investments in new production processes usually involve a significant amount of R&D, generating spillovers that lowers the second comer's investment cost. We show that these spillovers substantially affect the equilibrium of the dynamic game. Even for low spillover values, the leader delays her investment until the stochastic fundamental has gone past the level such that the follower's optimal strategy is to invest as soon as he attains the spillover. This bears several interesting implications. First, because the follower invests as he benefits from the spillover, in equilibrium the average time delay between the two investments is short, as it should be expected. Second, in case of a major innovation, an optimal public policy requires an intervention in favor of the investment activity; an increase in uncertainty - delaying the equilibrium - calls for higher subsidization rates. Third, numerical simulations show that the spillover reduces the difference between the leader's and the follower's maximum value functions. Accordingly, our model can help generate realistic market betas.     

Differentiated goods in a dynamic Cournot duopoly with emission charges on output

We extend the dynamic Cournot duopoly framework with emission charges on output by Mamada and Perrings (Econ Anal Policy 66:370–380, 2020), which encompassed homogeneous products in its original formulation, to the more general case of differentiated goods, in order to highlight the richness in its static and dynamic outcomes. Each firm is taxed proportionally to its own emission only and charge functions are quadratic. Moreover, due to an adjustment capacity constraint, firms partially modify their output level toward the best response. Like in Mamada and Perrings (Econ Anal Policy 66:370–380, 2020), the only steady state coincides with the Nash equilibrium, and it will be considered admissible when it guarantees the positivity of the marginal emission charge. We find that the full efficacy of the environmental policy, which applies to an equilibrium that is globally asymptotically stable anytime it is admissible, is achieved in the case of independent goods, as well as with a low good interdependence degree in absolute value, independently of being substitutes or complements. When goods are substitutes and their interdependence degree is high, the considered environmental policy is still able to reduce pollution at the equilibrium, but the latter is stable just when the policy intensity degree is large enough. When instead goods are complements and their interdependence degree is high in absolute value, the considered environmental policy produces detrimental effects on the pollution level and the unique equilibrium is always unstable, when admissible. This highlights that, from the static viewpoint, even in the absence of free riding possibilities, the choice of the mechanism to implement has to be carefully pondered, according to the features of the considered economy.

     

Optimal zoning of managerial duopoly

This paper investigates optimal zoning of two managerial firms in an unconstrained linear city. Comparing with the case in which firms are not managerial type, the strategic delegation increases the incentives of one firm to locate farther from the rival. Then, a welfare function is introduced to highlight zoning regulation as an influential competition policy tool. Depending on the regulator's objective function and the timing of location choice, we provide a new mechanism that allows the regulator to attain the optimal locations of managerial firms and can lead to strong or weak competition.     

Spatial duopoly with discriminatory pricing

The concept and existence of an equilibrium is established for profit maximizing competitors whose decisions involve choices of both delivered price schedules and firm locations. Each firm faces a production function; each is allowed to locate in the plane and to set discriminatory prices. Any transport cost function that is continuous in the firm location variable may be used. It is shown that the locations of the two firms are in equilibrium if each firm is minimizing social cost (i.e., the total cost to the firms of supplying the market with the good it demands is minimized) with respect to the opponent's fixed location.     

Endogenous timing in a mixed duopoly: price competition with managerial delegation

We introduce a managerial delegation contract into the mixed duopoly model and examine its influence on price setting in a mixed duopoly in the context of the endogenous‐timing problem. We obtain the result that owners of a public and a private firm prefer to delay the setting of the prices of their products as much as possible. Thus, in equilibrium, the firms choose their prices simultaneously in the latter stage of the game. This is in contrast to the findings of the entrepreneurial case, according to which firms choose prices simultaneously in the former stage. Copyright © 2009 John Wiley & Sons, Ltd.     

Equilibrium pricing and advertising strategies for nondurable experience products in a dynamic duopoly

The quality of many consumer nondurable goods or services is sufficiently complex or obscure that consumers cannot completely verify the true quality in a single usage. For such ‘experience’ products or services, the accumulated consumer consumption experience of a brand is an important determinant of its sales or market share. The market share of a brand is in turn directly influenced by its own and the competitive price and advertising strategies, given the different levels of quality (among other factors). In this paper, we investigate the impact of the aggregate consumption experience on the firm's dynamic pricing and advertising strategies by developing a formal game-theoretic model of a dynamic duopoly. The model of competition does not yield explicit closed-form expressions for the dynamic price and advertising paths of the two firms. Hence, we simulate the equilibrium paths using a discrete-time algorithm. Our simulation results provide interesting insights into the dynamic equilibrium price and advertising paths, under a variety of realistic competitive scenarios.     

Robust games: theory and application to a Cournot duopoly model

In this paper, the robust game model proposed by Aghassi and Bertsimas (Math Program Ser B 107:231–273, 2006) for matrix games is extended to games with a broader class of payoff functions. This is a distribution-free model of incomplete information for finite games where players adopt a robust-optimization approach to contend with payoff uncertainty. They are called robust players and seek the maximum guaranteed payoff given the strategy of the others. Consistently with this decision criterion, a set of strategies is an equilibrium, robust-optimization equilibrium, if each player’s strategy is a best response to the other player’s strategies, under the worst-case scenarios. The aim of the paper is twofold. In the first part, we provide robust-optimization equilibrium’s existence result for a quite general class of games and we prove that it exists a suitable value \(\epsilon \) such that robust-optimization equilibria are a subset of \(\epsilon \)-Nash equilibria of the nominal version, i.e., without uncertainty, of the robust game. This provides a theoretical motivation for the robust approach, as it provides new insight and a rational agent motivation for \(\epsilon \)-Nash equilibrium. In the last part, we propose an application of the theory to a classical Cournot duopoly model which shows significant differences between the robust game and its nominal version.