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The purpose of this study is to analyze comparatively the properties of open-loop and closed-loop equilibria in a dynamic oligopoly model with price dynamics and reflexive behavior of market agents.

To consider dynamic competitive markets, the authors focus on a differential game theory in oligopolistic structures, using analytical models to illustrate how advertising effort, good differentiation and price stickiness interact simultaneously in the open-loop and the closed-loop Nash equilibria. The comparative assessment of these equilibria obtains some significant results.

An optimization model that enriches the continuous time is presented. Under the open-loop and the closed-loop, Nash equilibrium showed an increase in the total output, advertising in price stickiness and promotional efficiency, while there was a decrease in product differentiation and advertising promotional efficiency. However, the open-loop equilibrium levels are larger than the closed-loop equilibrium. Under the closed-loop information, the long-run equilibrium was faster than the opened-loop in a dynamic oligopoly. The graphical illustration was used to present the behavior of the model parameters.

This study helps managers to choose an appropriate price and advertising adjustment to maximize profit. The obtained results may help firms to make the smart decision and may provide managers the valuable tool for making decisions in the competitive market environments.

This is a first attempt to analyze a dynamic oligopoly in the differentiated market environment. It considers a joint action of the output and advertising in shaping the closed-loop and the open-loop equilibria with N competitors in a dynamic competitive setting.

This study considered the dynamic equilibrium decision-making problem in a three-level supply chain comprising a manufacturer, a recycler and an echelon utilization (EchU) enterprise under the condition of cost-sharing coordination.

This study constructed a differential game model based on cost-sharing coordinated decision-making among a manufacturer, a recycler and an EchU enterprise operating under a cost subsidy. The study determined the optimal equilibrium strategies and evolutionary characteristics of subsidy mechanisms in a closed-loop supply chain. Finally, this study numerically simulated the path evolution process of vehicle battery EchU, the profit of each stakeholder and the sensitivity of parameters and verified the influences of various parameters on the overall structure and path.

The results show that a cost subsidy policy has a moderating effect on the EchU decision-making process and supply chain profit. The effect of that policy increases over time.

This study determined the equilibrium decision-making of enterprises in a closed-loop vehicle battery supply chain from a dynamic perspective, as well as the combined effects of government subsidy policies and cost-sharing coordination mechanisms.

The results have important guiding significance for coordination and cooperation between enterprises in closed-loop supply chains, for their decision-making and for the development of government subsidies.

This study considered the effects of government subsidies on closed-loop supply chains and the introduction of an EchU market to a closed-loop vehicle battery supply chain.

The purpose of this paper is to study how the government stimulates incineration plants to participate in waste classification management, and how to adjust the subsidy strategy for them.

Considering that the classification behavior of residents will produce herd effect, and waste classification can reduce the disposal cost of incineration plants, the authors constructed a differential game model between the government and waste incineration plants, and analyzed the input strategy of the government and incineration plants when they cooperate in the management of municipal waste classification.

Increasing the input level of supervision or raising subsidy price, the government can promote incineration plants to increase the input level of incentive. Moreover, from a long-term perspective, increasing the input level of supervision is more effective. Compared with government supervision, the method of incineration plants incentive can more effectively increase the amount of waste disposal. Furthermore, the government supervision and the incineration plants incentive have a positive interaction effect on improving the amount of waste disposal. Increasing the input level of incineration plants incentive or the level of waste-to-energy technology can increase the amount of waste disposal, and from a long-term perspective, increasing the level of R&D investment is more beneficial to increasing the amount of waste disposal.

The results are helpful to improve the investment in the management of waste classification, and also provide a certain theoretical basis for the government's subsidy policy for incineration plants, so as to reduce the financial pressure of the government.

After receiving advertising messages, most consumers rarely purchase the advertised products at once, which results in a delay between advertising exposure and its effect. This paper is devoted to exploring the advertising decision and coordination issues for a supply chain system subject to advertising immediate and delayed effects.

By applying the game theory, the differential game models with delay are constructed for the supply chain to examine the equilibrium advertising efforts, brand goodwill and the optimal profits under the different cooperation situations. A class of transfer payment contracts is designed to achieve the best outcome of the supply chain. Illustrative examples are given to demonstrate the effectiveness of addressed results and provide some managerial perspectives.

It can be found that the complete cooperation situation can stimulate the advertising investment, drive the product demand and improve the economic profit. Also, a class of transfer payment contracts is designed in this paper, such that the supply chain can perfectly realize the profit maximization, and each member can achieve the Pareto improvement.

This work does not address the random market environment, which can be filled in the future. Furthermore, this paper has been done in a single supply chain structure. It is an interesting future line of research when taking competitive behavior (e.g. competition among manufacturers, retailers or supply chains) into account.

This study will help managers make advertising strategies, advise an optimal cooperation way and design the coordination contracts to ensure the economic development of the supply chain. These obtained conclusions may provide a valuable decision-support for marketing management.

For a supply chain, the most previous literature about dynamic advertising models focused on a single advertising effect-immediate effect. This work explores advertising strategy with double advertising effects and investigates the coordinating power of new transfer payment contracts.

As the quality of the environment decreases, enterprises and consumers' awareness of environmental protection is constantly improving. More and more enterprises begin to increase their investment in carbon emission reduction and attract environmentally friendly consumers to buy low-carbon products through advertising. The purpose of this paper is to utilize a realistic differential game model to provide dynamic carbon emission reduction strategies, advertising strategies and cooperation methods for complex supply chain members from a long-term perspective.

This paper uses the extend Vidale-Wolfe model (V-W model) to discuss the dynamic joint emission reduction strategy in the supply chain.

(1) When consumers' awareness of environmental protection increases, on the whole, carbon emission reduction and profit of products show an upward trend. (2) From a long-term perspective, the manufacturer's advertising subsidy to one of the retailers is the best choice. If the strength of the two retailers is unbalanced, the manufacturer will choose to cooperate with the dominant retailer. (3) Advertising, as a marketing means for retailers to promote low-carbon products, can alleviate the adverse effects of prisoner's dilemma in a semi-cooperative state, but it cannot achieve the Pareto optimization result.

This paper focuses on the analysis of the situation that when the manufacturer is the leader and thinks that consumers are active advocates of low-carbon products.

The results of this paper can provide theoretical basis for the joint emission strategy of supply chain members in low-carbon environment.

This paper examines the profit distribution of engineering projects in the integrated project delivery (IPD) mode. IPD is a new delivery method that can ameliorate many of the disadvantages of traditional delivery methods and improve project results. In the implementation of IPD, the profit distribution is key for ensuring the success of IPD projects.

This paper described a new method for characterizing profit distribution in the IPD mode. The payment function and Shapley value of the cooperative fuzzy game of fuzzy alliance were defined by considering the Choquet integral of the fuzzy measure. The participation of each player was considered, and the influence of participation on the profit distribution was discussed. Lastly, changes in the profit distribution of core participants under different alliance combinations were studied.

A case from a report of The American Institute of Architects (AIA) was used to verify the fuzzy alliance model. There was a significant correlation between the degree of participation of the owner, architect and builder and the profit distribution among these three participants.

The theoretical research in this paper has some limitations. Initially, this paper selects a case with only three key participants in order to simplify the research. When there are many core participants, how to establish the alliance in the IPD mode and how to establish the corresponding profit distribution model, further work is certainly required to disentangle these complexities in models. Second, in this case, BIM technology has little impact on the income of the whole project. Therefore, this paper does not consider the impact of BIM technology on the marginal effect of the IPD project. Third, the contract type in the case is a custom tri-party based on IFOA. There is no classified discussion of the impact of different contracts on the profit distribute in the paper.

Based on the in-depth study of cooperative game with alliance structure, this paper promotes the classic cooperative game with alliance structure. The authors define the payoff function of fuzzy cooperative games by Choquet integral of fuzzy measure, and introduce the idea into the field of IPD. It aims at extending the solution to a cooperative game without a core. It can be obtained through a simple calculation. In the IPD alliance, the fuzziness and uncertainty of the participation degree of each participant will affect the profit of the whole project. The authors find that the higher the participation rate of players, the more profit each participant has. The greater the influence weight of the designer on the alliance, the lower the influence weight of the contractor on the alliance, the lower the participation of the contractor and the designer, and the lower the income distribution value of the three core participants. It shows a monotonous decline status.

For any construction enterprise, it can make more profits if it joins the grand alliance. In the IPD alliance, each participant can maximize their own interests, which can also promote the enthusiasm of construction enterprises to participate in the alliance and increase the application of IPD mode in AEC industry. This research method provides a new fast, effective, and more realistic solution method for cooperative countermeasures. It can be further extended to other cooperative game fields and advance a new research perspective and solution for the distribution of cooperative interests.

The contribution of this paper is the development of a fuzzy alliance model that provides a tool for measuring the profit distribution in IPD. This is the first quantitative model to connect the degree of participation with the profit distribution in IPD using fuzzy alliance.

Real estate developers often operate in oligopolistic environments. Pricing strategies must be made in an interactive framework that makes empirical evaluation difficult. This study appeals to economic experiments to examine how developers price their properties, especially when there is an option to market pre‐completed units. In addition, the interaction between bidding for land and pricing the end product is examined. The results indicate that competitor actions are important considerations in pricing decisions. In particular, the profit maximizing pricing strategy depends critically on being competitive, not necessarily being the most aggressive. Interestingly, pre‐completed units sell only at prices that incorporate future price expectations, and successful bids tend to precipitate more aggressive pricing. Finally, competitive bidding and pricing strategies appear to the best profit maximizing strategy.

The purpose of this paper is to research stochastic dynamic investment games with stochastic interest rate model in continuous time between two investors. The market interest rate has the dynamics of Duffie‐Kan interest rate.

Recently, there has been an increasing interest in financial market models whose key parameters, such as the bank interest rate, stocks appreciation rates, and volatility rates, are modulated by stochastic interest rate. This paper uses the Duffie‐Kan stochastic interest rate model to develop stochastic differential portfolio games. By the HJB optimality equation, a general result in optimal control for a stochastic differential game with a general utility payoff function is obtained.

Derive a general result in optimal control for a stochastic differential game with a general utility payoff function. The explicit optimal strategies and value of the games are obtained for the constant relative risk aversion utility games of fixed duration.

Accessibility and availability of stochastic interest rate data are the main limitations, which apply.

The results obtained in this paper could be used as a guide to actual portfolio games.

This paper presents a new approach for the optimal portfolio model under compound jump processes. The paper is aimed at actual portfolio games.

Determining the optimal capital structure becomes more complicated by the presence of an agency problem. The issuance of debt as a corporate governance mechanism introduces the asset substitution problem – the agency cost of debt. Thus, there is a recognized need for models that can resolve the agency problem between the debtholder and the manager who acts on behalf of the shareholder, leading to optimal capital structure choice, and enhanced firm value. The purpose of this paper is to model the debtholder-manager agency problem as a dynamic game, resolve the conflicts of interests and determine the optimal capital structure.

As there is no satisfactory model for dealing with the above issues, this paper uses a differential game framework to analyze the incongruity of interests between the debtholder and the manager as a non-cooperative dynamic game and further resolves the conflicts of interests as a cooperative game via a Pareto-efficient outcome.

The optimal capital structure required to minimize the marginal cost of the agency problem is a higher use of debt, lower cost of equity and withheld capital distributions. The debtholder is also able to enforce cooperation from the manager by providing a lower and stable cost of debt and a greater debt facility in the overtime framework.

The study develops a new dynamic contract theory model based on the integrated issues of capital structure, corporate governance and agency problems and applies the differential game approach to minimize the agency problem between the debtholder and the manager.

The objective of this paper is to investigate the impact of the information sharing of the dynamic demand on green technology innovation and profits in supply chain from a long-term perspective.

The authors consider a supply chain consisting of a manufacturer and a retailer. The retailer has access to the information of dynamic demand of the green product, whereas the manufacturer invests in green technology innovation. Differential game theory is adopted to establish three models under three different scenarios, namely (1) decentralized decision without information sharing of dynamic demand (Model N-D), (2) decentralized decision with information sharing of dynamic demand (Model S-D) and (3) centralized decision with information sharing of dynamic demand (Model S-C).

The optimal equilibrium results show that information sharing of dynamic demand can improve the green technology innovation level and increase the green technology stocks only in centralized supply chain. In the long term, the information sharing of dynamic demand can make the retailer more profitable. If the influence of green technology innovation on green technology stocks is great enough or the cost coefficient of green technology innovation is small enough, the manufacturer and decentralized supply chain can benefit from information sharing. In centralized supply chain, the value of demand information sharing is greater than that of decentralized supply chain.

The authors used game theory to investigate demand information sharing and the green technology innovation in a supply chain. Specially, the demand information is dynamic, which is a variable that changes over time. Moreover, our research is based on a long-term perspective. Thus, differential game is adopted in this paper.