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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.

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 purpose of this paper is to address the issue of optimal management of ecosystems by developing a dynamic model of strategic behavior by users/communities of an ecosystem such as a lake, which is subject to pollution resulting from the users. More specifically, it builds a model of two ecosystems that are spatially connected.

The paper uses the techniques of optimal control theory and game theory.

The paper uncovers sufficient conditions under which the analysis of the dynamic game can be converted to an optimal problem for a pseudo authority. It is shown that if the discount rate on the future is high enough relative to ecological self‐restoration parameters then multiple stable states appear. In this case, if the pollution level is high enough it is too costly in terms of what must be given up today to restore the damaged system. By using computational methods, the paper evaluates the relative strengths of lack of coordination, strength of ecosystem self‐cleaning forces, size of discount rates, etc.

The methodology as well as findings can help to devise an optimal management strategy over time for ecosystems.

The purpose of this paper is to examine the impacts of advertising expenditure on brands' market shares, utilizing a novel four‐week advertising‐sales data from the highly competitive oligopolistic Finnish beer market in which price competition among the homogeneous larger‐type beer brands is not allowed during the period of the study.

Competition is modelled using the Lanchester model. The impacts of advertising on market shares are estimated using the impulse‐response functions from vector autoregression, and the full information maximum likelihood and advertising elasticities.

Some new insights into beer market dynamics are obtained. First, the impacts of advertising are not similar across brands. Second, overspills of advertising impacts across brands are detected. Third, the reactions to competitors' advertising attacks are mild.

The paper utilizes four‐week brand‐level data on the market shares of the leading beer brands in Finland and the brands' advertising expenditure. During the period of the data, price competition is not allowed, which creates a unique opportunity to study the impacts of advertising on the market shares of brands.

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.

We take a differential game approach to study the optimal choices of managerial firms concerning efforts in product a process innovation. We find the Nash equilibria under the open-loop and closed-loop information structure, and we compare the steady state allocations with the corresponding equilibria of markets populated by standard profit-maximising firms. We find that the managerial incentive leads firm to underinvest in product differentiation and to overinvest in process innovation, as compared to standard profit-maximising firms.

The authors characterize the conditions under which a country may eventually split and when it splits within an infinite horizon multi-stage differential game.

In contrast to the existing literature, the authors do not assume that after splitting, players will adopt Markovian strategies. Instead, the authors assume that while the splitting country plays Markovian, the remaining coalition remains committed to the collective control of pollution and plays open-loop.

Within a full linear-quadratic model, the authors characterize the optimal strategies. The authors later compare with the outcomes of the case where the splitting country and the remaining coalition play both Markovian. The authors highlight several interesting results in terms of the implications for long-term pollution levels and the duration of coalitions under heterogenous strategies as compared to Markovian behavior.

In this paper, the authors have illustrated the richness of the simplications of enlarging the set of strategies in terms of the emergence of coalitions, their duration and the implied welfare levels per player. Varying only three parameters (the technological gap, pollution damage and coalition payoff share distribution across players), the authors have been able to generate, among other findings, quite different rankings of welfare per player depending on whether the remaining coalitions after split play Markovian or stay precommited to the pre-splitting period decisions.

Assesses the place of Heinrich von Stackelberg in the history of ideas as reflected in the literature of economics. Uses evidence from three main sources: histories of economics, the periodical literature and doctoral dissertations to support the conclusion that Stackelberg already has an important and lasting place in the history of economic thought. Points out that the use of Stackelberg’s ideas and techniques is now as general and common as the use of those of Cournot, Walras, Pareto and Nash. Presents a short section devoted to his views on state control because these are so often misunderstood. Speculates on possible reasons why Stackelberg is not ranked more highly than he usually is.