Identical Marginal Costs Research Articles

Analysis of the stability and the bifurcations of two heterogeneous triopoly games with an isoelastic demand

<abstract><p>In this paper, we explore two heterogeneous triopoly games where the market demand function is isoelastic. The local stability and the bifurcations of these games are systematically analyzed using a symbolic approach, proposed by the author, of counting real solutions of a parametric system. The novelty of our study is twofold. On one hand, we introduce into the study of oligopoly games several methods of symbolic computation, which can establish analytical results and are different from the existing methods in the literature based on numerical simulations. In particular, we obtain the analytical conditions of the local stability and prove the existence of double routes to chaos through the period-doubling bifurcation and the Neimark-Sacker bifurcation. On the other hand, in the special case of the involved firms having identical marginal costs, we acquire the analytical conditions of the local stability for the two models. By further analyzing these conditions, it seems that the presence of the local monopolistic approximation (LMA) mechanism has a stabilizing effect for heterogeneous triopoly games with the isoelastic demand.</p></abstract>

Firms’ strategic delegation with heterogeneous consumers

We revisit firms’ strategic delegation in a Cournot game. We consider a market comprising two consumer groups, with either a high or low willingness to pay. In this market, we first consider firms’ identical marginal costs and show that either/both firms’ owners may strategically abandon the delegation option to avoid price collapse. We find three types of delegation decisions with either/both/no firm delegating in equilibrium. We further consider firms’ asymmetric marginal costs and show that the asymmetric equilibrium wherein only the less efficient firm delegates will exist in a wider parameter range, compared to that wherein only the more efficient firm delegates. Moreover, delegation may enable the less efficient firm to achieve a higher profit than her rival.

On the coalitional stability of monopoly power in differentiated Bertrand and Cournot oligopolies

In this article, we revisit the classic comparison between Bertrand and Cournot competition in the presence of a cartel of firms that faces outsiders acting individually. This competition setting enables to deal with both non-cooperative and cooperative oligopoly games. We concentrate on industries consisting of symmetrically differentiated products where firms operate at a constant and identical marginal cost. First, while the standard Bertrand–Cournot rankings still hold for Nash equilibrium prices, we show that the results may be altered for Nash equilibrium quantities and profits. Second, we define cooperative Bertrand and Cournot oligopoly games with transferable utility on the basis of their non-cooperative foundation. We establish that the core of a cooperative Cournot oligopoly game is strictly included in the core of a cooperative Bertrand oligopoly game when the number of firms is lower or equal to 25. Moreover, we focus on the aggregate-monotonic core, a subset of the core, that has the advantage to select point solutions satisfying both core selection and aggregate monotonicity properties. We succeed in comparing the aggregate-monotonic cores between Bertrand and Cournot competition regardless of the number of firms. Finally, we study a class of three-firm oligopolies with asymmetric costs in which the core inclusion property mentioned above still holds. We also provide numerical examples to illustrate the difficulty to generalize this result to an arbitrary number of firms because of negative equilibrium quantities.

A distributed economic control and transition between economic and non-economic operation in islanded microgrids

In islanded microgrids, traditional droop control tends to make the total operating costs higher as the power is distributed by capacity ratios of distributed energy resources (DERs). According to equal increment rate criteria, to minimize the whole expenses, an interesting marginal costs-based economic droop control is proposed in this paper, and the active power can be distributed by identical marginal costs among DERs under economic droop control. If some DERs have arrived at the maximum or minimum power, consensus-based “virtual” controller is applied to make marginal costs still be the same among the rest of DERs. Moreover, distributed secondary frequency controller (DSFC) is proposed to rapidly restore system frequency to the nominal value. As an ancillary service, the whole design can easily realize the transition between economic and non-economic operation only by altering the type of droop control. The above controllers only need to interact with neighbor DERs by sparse communication network, so that eliminating the necessity of a central controller. An islanded microgrid incorporating renewable generators, storage devices and conventional generators are presented to verify the effectiveness of the above controllers. Simulation results show that the proposed controllers can successfully make islanded microgrids realize economic operation and the above transition.

Adaptive Marginal Costs-Based Distributed Economic Control of Microgrid Clusters Considering Line Loss

When several microgrids (MG) are interconnected into microgrid clusters (MGC), they have great potential to improve their reliability. Traditional droop control tends to make the total operating costs higher as the power is distributed by capacity ratios of distributed energy resources (DERs). This paper proposes an adaptive distributed economic control for islanded microgrids which considers line loss, specifically, an interesting marginal costs-based economic droop control is proposed, and consensus-based adaptive controller is applied, to deal with power limits and capacity constraints for storage. The whole expense can be effectively lowered by achieving identical marginal costs for DERs in MGC. Specially, the capacity constraints only for storages are also included to do further optimization. Moreover, consensus-based distributed secondary controllers are used to rapidly restore system frequency and voltage magnitudes. The above controllers only need to interact with neighbor DERs by a sparse communication network, eliminating the necessity of a central controller and enhancing the stability. A MGC, incorporating three microgrids, is used to verify the effectiveness of the proposed methods.

Correlated equilibria in homogeneous good Bertrand competition

We show that there is a unique correlated equilibrium, identical to the unique Nash equilibrium, in the classic Bertrand oligopoly model with homogeneous goods and identical marginal costs. This provides a theoretical underpinning for the so-called “Bertrand paradox” as well as its most general formulation to date. Our proof generalizes to asymmetric marginal costs and arbitrarily many players in the following way: The market price cannot be higher than the second lowest marginal cost in any correlated equilibrium.

The Optimum Discriminatory Tariffs under the Cournot-Nash Strategy in International Trade

This paper investigates the optimum ad valorem tariffs under the Cournot competition. There are three situations that exceptions to most-favored-nation (MFN) principle are made within the GATT framework: free trade agreement, ‘safeguard’ actions and escape clause. Hence, the issue of discriminatory tariffs has important policy implications. Most of the literature concerning the discriminatory tariffs assumes that the objective of the government is to maximize their country’s welfare by choosing the appropriate trade policy. We expand welfare-maximizing to loss-minimization model in order to comparing two types of optimum discriminatory tariff ratios. In the loss-minimization model, we assume that the objective of the government is to minimize loss in consumers’ surplus while subject to a minimum target level of tariff revenue. The aim of this paper is to show that the optimum ad valorem tariff ratio between two exporting countries can be unambiguously derived with a linear demand curve and constant marginal costs. We conclude that the welfare-maximizing tariff ratio differs from that of the loss-minimization model or a quasi-Ramsey rule. The Ramsey-like tariff ratio does not depend on the size of the intercept of market demand since its objective function is to minimize the loss in consumers’ surplus. On the contrary, the welfare-maximizing tariff ratio is dependent on the intercept since it is used to measure the total consumers’ surplus. Only when the two foreign producers have the identical marginal cost will they coincide.

On hierarchical competition in oligopoly

In this paper, we consider a hierarchical oligopoly model, in which firms compete on quantities of an homogeneous product. We provide a proof and an interpretation that under the three necessary and sufficient conditions of linear aggregate demand, constant and identical marginal costs, the strategy of leaders at any stage depends neither on the number of leaders who play after nor on the number of remaining stages. So, all firms behave as Cournotian oligopolists on the residual demand. We show that these three assumptions are not only sufficient but also necessary. Any departure from any of these assumptions rules out this property.