Shared Manufacturing in A Differentiated Duopoly with Capacity Constraints

This study sets up a differentiated duopoly model considering capacity constraints and shared manufacturing, investigates the equilibrium results, examines the effects of product differentiation and capacity constraints in three scenarios, and compares the equilibrium outcomes in three cases under Cournot and Stackelberg competition. We find that capacity constraints affect the relationships among product differentiation, equilibrium results, and the market share of enterprises. Shared manufacturing impacts the degree of excess capacity, profits, consumer surplus, and social welfare; however, it may sometimes play a negative role in alleviating excess capacity. Moreover, Cournot competition is a better choice for enterprises with capacity constraints compared to Stackelberg competition.

CAPACITY SHARING STRATEGY WITH SUSTAINABLE REVENUE-SHARING CONTRACTS

This paper develops a duopoly model to analyse capacity sharing strategy and the optimal revenue-sharing contract under a two-part tariff and examines the effects of capacity sharing, cost, and sharing charges in three scenarios. The paper uses the two-part tariff method and adds a more realistic assumption of incremental marginal costs to improve the research on capacity sharing strategies. The results show that capacity constraints affect the sustainable development of firms. A sustainable revenue-sharing contract can create a win-win situation for both firms and promote capacity sharing. Capacity sharing, cost, and the revenue-sharing rate have different impacts in different scenarios; the optimal revenue-sharing rate and fixed fee can be determined to maximise the profits of firms that share capacity. However, capacity sharing may not improve social welfare.

Video Platforms’ Value-Added Service Investments and Pricing Strategies for Advertisers

Using a game-theoretical approach, this paper develops a duopoly model and examines value-added service (VAS) investments and pricing strategies on video platforms with opposite inter-group network externalities between two groups. We consider two scenarios with VAS investment, namely, a single platform investing in VASs for advertisers (S-Model) and both platforms investing in VASs for advertisers (B-Model). We found the following: (i) In the S-Model, the investing platform’s VAS level remains maximum when the marginal investing cost is low; otherwise, it decreases with the cost. Investing and non-investing platforms’ advertising prices are unaffected by the marginal investing cost if the cost is low; otherwise, the prices decrease and increase with the cost, respectively. Furthermore, the investing platform’s advertising price is higher than the non-investing platform’s. (ii) In the B-Model, the two platforms’ VAS levels remain maximum if the marginal investing cost is low; otherwise, they decrease with the cost. The two platforms’ advertising prices are equal and irrelevant to the marginal investing cost. (iii) The investing platform’s VAS level in the S-Model is higher than or the same as that in the B-Model and the investing platform’s advertising price in the S-Model is higher than that in the B-Model. (iv) Compared to the scenario without VAS investment, the investing platform’s advertising price is higher in the S-Model, but the same in the B-Model.

Environmental Management through Coopetitive Urban Waste Recycling in Eco-Industrial Parks

In this article, we consider the coexistence of competing actors within a specific eco-industrial park. The competing firms dynamics evolves by means of an interplay agreement determined among the competitors themselves. In particular, we show a possible scenario in which the selected eco-industrial competitors could greatly benefit from a coopetitive interaction, within their common eco-park, while improving the general conditions of a near residential area. The associated dynamical coopetitive agreement, aims at the growth and improvement of the firms themselves and of their industrial network (within a virtuous environmental path). As an example, we assume the existence of two competitors selling the same good on the same market, so that, from a competitive point of view, we construct a classic Cournot duopoly model upon which we build up a multidimensional coopetitive agreement. Our eco-friendly deal allows to “enlarge the pie” of possible gains by diminishing sunk costs and other forms of costs, especially the environmental costs associated to the management of urban waste recycling. Consequently, we suggest production methods and production quantitative profiles in order to “share the gains fairly”. We show a complete mathematical analysis of our new economic game and show some of its possible and relevant solutions.

Self-Enforcing Price Leadership

A dynamic Bertrand-duopoly model where price leadership emerges in equilibrium is developed. In the price leadership equilibrium, a firm leads price changes and its competitor always matches in the next period. The firms produce a homogeneous product and are identical except for the information they possess about demand. The market size follows a two-state Markov process. Market size realizations are observed by one of the firms but not the other. Without explicit communication, price leadership allows firms to jointly approximate monopolistic profits in equilibrium as the market size becomes more persistent provided that firms are patient. In the presence of persistent market dynamics, the informed firm’s price serves as a signal of current and therefore future market conditions. In the proposed price leadership equilibrium, the informed firm could cut prices without being detected, but it does not do so because it would lead the uninformed to also lower their price in the following period.

The Impacts and Decision of Community-friendly Corporate Social Responsibility Based on the Duopoly Model

There are multiple relationships between enterprises and communities, and the community-friendly corporate social responsibility (CSR) is unique. This paper constructs a duopoly model composed of two enterprises and a community, examines the impacts of community-friendly CSR on stakeholders, and analyzes the CSR decision. The results show that the level of community-friendly CSR, negative externalities, tax rate, and consumer sensitivity have multiple effects on profits, consumers, and social welfare, and the impacts of each factor are affected by the other factors; whether the competitors implement CSR affect the CSR decision of the other one; under certain circumstances, the implementation of CSR is conducive to achieving a win-win situation for the enterprises and the community.

Strategic trade policy with interlocking cross-ownership

By analysing interlocking cross-ownership, this work reconsiders the inefficiency of activist governments that set subsidies for their exporters (Brander and Spencer, J Int Econ 18:83–100). Making use of a third-market Cournot duopoly model, we show that the implementation of strategic trade policy in the form of a tax (subsidy) when goods are differentiated (complements) is Pareto-superior to free trade within precise ranges of firms’ cross-ownership, richly depending on the degree of product competition. These results challenge the conventional ones in which public intervention (1) is always the provision of a subsidy and (2) always leads to a Pareto-inferior (resp. Pareto-superior) equilibrium when products are substitutes (resp. complements).

Dynamics of a Heterogeneous Constraint Profit Maximization Duopoly Model Based on an Isoelastic Demand

A Cournot duopoly game is a two-firm market where the aim is to maximize profits. It is rational for every company to maximize its profits with minimal sales constraints. As a consequence, a model of constrained profit maximization (CPM) occurs when a business needs to be increased with profit minimal sales constraints. The CPM model, in which companies maximize profits under the minimum sales constraints, is an alternative to the profit maximization model. The current study constructs a duopoly game based on an isoelastic demand and homogeneous goods with heterogeneous strategies. In the event of sales constraint and no sales constraint, the local stability conditions of the Cournot equilibrium are derived. The initial results show that the duopoly model would be easier to stabilize if firms were to impose certain minimum sales constraints. Two routes to chaos are analyzed by numerical simulation using 2D bifurcation diagram, one of which is period doubling bifurcation and the other is Neimark–Sacker bifurcation. Four forms of coexistence of attractors are demonstrated by the basin of attraction, which is the coexistence of periodic attractors and chaotic attractors, the coexistence of periodic attractors and quasiperiodic attractors, and the coexistence of several chaotic attractors. Our findings show that the effect of game parameters on stability depends on the rules of expectations and restriction of sales by firms.

Duopoly price competition with limited capacity

We study a variation of the duopoly model by Kreps and Scheinkman (1983). Firms limited by their capacity of production engage in a two stage game. In the first stage they commit to levels of production not exceeding their capacities which are then made common knowledge. In the second stage after production has taken place firms simultane- ously compete in prices. Solution of this sequential game shows that the unique Cournot equilibrium outcome as in Kreps and Scheinkman is not always guaranteed. However the Cournot outcome is still robust in the sense that given sufficiently large capacities this equilibrium holds. If capacities are sufficiently small, firms decide to produce at their full capacity and set a price which clears the market at the given level of output.