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The purpose of this paper is to provide a framework to help business marketers with a mixed online and traditional retail channel (multi‐channel company) to find the optimal pricing strategy and market structure in order to maximize their profits.

A game theory model is developed to determine the optimal pricing strategy for the multi‐channel company.

It was demonstrated that an optimal pricing strategy exists under different market structures for a multi‐channel company. When a company uses multiple channels to sell its product, the optimal pricing strategy is to use a low‐high pricing strategy if the online marginal cost is equal to or less than the traditional marginal cost, or a high‐low pricing strategy if the online marginal cost is far larger than the traditional marginal cost. Furthermore, in order to maximize its profit, the company using multiple channels should adopt channel integration as the optimal market structure.

The present study assumed that all consumers have perfect information. However, information with the consumers could be incomplete. It is recommended that future research explore the pricing strategy under incomplete information settings.

The paper provides a very useful model framework, pricing strategy, and market structure for business managers who are using or planning to use multiple channels to sell their products.

This paper fills a conceptual and practical gap for a structured analysis of the current state of knowledge about multi‐channel pricing strategies. It provides practical and solid advice and examples demonstrating the application of the different types of pricing strategies for business managers.

The purpose of this paper is to provide a framework to help competitive firms find optimal pricing and brand management strategies in order to maximize their respective profits.

A game‐theoretic model is developed to determine optimal pricing and brand management strategies for competitive firms.

The study demonstrates that optimal pricing and brand management strategies exist for firms in a competitive market. The optimum marketing strategy for competitive firms to employ is the cooperative alliance pricing and brand management strategy, particularly when market competition is very intense.

The present study assumes that all information is known to all parties. However, information could be incomplete. It is recommended that future research explore pricing and brand management strategies under incomplete and asymmetric information settings.

The paper provides a very useful model framework and pricing and brand management strategy for business managers when they are doing business in a competitive market.

The paper fills a conceptual and practical gap for a structured analysis of the current state of knowledge about alliance brand. It provides practical and solid advice and examples demonstrating the application of cooperative alliance pricing and brand management strategies for business managers.

Using Brandenburger and Nalebuff's 1995 co‐opetition model as a reference, the purpose of this paper is to seek to develop a tool that, based on the tenets of classical game theory, would enable scholars and managers to identify which games may be played in response to the different conflict of interest situations faced by companies in their business environments.

The literature on game theory and business strategy are reviewed and a conceptual model, the strategic games matrix (SGM), is developed. Two novel games are described and modeled.

The co‐opetition model is not sufficient to realistically represent most of the conflict of interest situations faced by companies. It seeks to address this problem through development of the SGM, which expands upon Brandenburger and Nalebuff's model by providing a broader perspective, through incorporation of an additional dimension (power ratio between players) and three novel, respectively, (rival, individualistic, and associative).

This proposed model, based on the concepts of game theory, should be used to train decision‐ and policy‐makers to better understand, interpret and formulate conflict management strategies.

A practical and original tool to use game models in conflict of interest situations is generated. Basic classical games, such as Nash, Stackelberg, Pareto, and Minimax, are mapped on the SGM to suggest in which situations they could be useful. Two innovative games are described to fit four different types of conflict situations that so far have no corresponding game in the literature. A test application of the SGM to a classic Intel Corporation strategic management case, in the complex personal computer industry, shows that the proposed method is able to describe, to interpret, to analyze, and to prescribe optimal competitive and/or cooperative strategies for each conflict of interest situation.

With the rapid growth of the economy, people have increasingly higher living standards, and although people simply pursued material wealth in the past, they now pay more attention to material quality and safety and environmental protection. This paper discusses the lack of motivation for investing in fresh-keeping technology for agricultural products by individual members of an agricultural supply chain composed of a supplier and a retailer by means of mathematical models and data simulations and discuss the optimal price-invest strategies under different sales models.

First, based on the model of no investment by both sides (NN), this paper considers three models: supplier only (MN), retailer only (NR) and cooperative investment (MR). Then, the authors analyze the influence of consumer price sensitivity and freshness sensitivity on the investment motivation of agricultural products under four models. Subsequently, the paper makes a sensitivity analysis of the optimal strategies under several models, and makes a game analysis of the suppliers and retailers of agricultural products. Finally, we conduct an empirical analysis through specific values.

The results show that (a) when the two sides cooperate, the amount of investment is largest, the freshness of the agricultural products is highest, and the sales volume is greatest; however, when both sides do not invest, the freshness of agricultural products and sales volume are lowest. (b) The price and freshness sensitivity of the consumer have an impact on investment decisions. Greater freshness sensitivity corresponds to a higher investment, higher agricultural product price, greater sales volume, and greater supply chain member income and overall income; however, greater price sensitivity corresponds to a lower investment, lower agricultural product price, lower sales volume, fewer supply chain members and lower overall income. (c) The investment game between the supplier and retailer is not only related to the sensitivity to price and freshness but also to the coordination coefficients of interest. At the same time, the market position of agricultural products should be considered when making decisions. The market share of agricultural products will affect the final game equilibrium and then affect the final benefit of the supply chain and individual members.

These results provide managerial insights for enterprises preparing to invest in agricultural products preservation technology.

At present, the main problem is that member enterprises of agricultural supply chains operate based on their own benefits and are resistant to investing alone to improve the freshness of agricultural products. Instead, they would prefer that other members invest so that they may reap the benefits at no cost. Therefore, the enterprises in each node of the agricultural product supply chain are not motivated enough to invest, and competition and game states are observed among them, and such behavior is definitely not conducive to improving the freshness of agricultural products. However, the current research on agricultural products is more about price, quality and greenness, etc., and there are few studies on agricultural investment. Through the establishment of the model, this paper is expected to provide theoretical suggestions for the supply chain enterprises that plan to invest in agricultural products preservation technology.

Price‐taking has long been mistakenly regarded as an inferior firm behavior in an imperfectly competitive market. This scenario is challenged when a “Naiver’s Paradox” is shown to exist in an oligopolic market where all firms produce the same product with the same technology (cost structure). It is shown that a firm behaving as a naive price‐taker with ignorance of its output impact on the market will perform no worse or even better than its rivals in terms of profits achieved, where the latter are assumed to take “Cournot”, “relative profit” or other more advanced strategies. More significantly, when the number of firms in the market is large, a price‐taker may achieve higher profit not only in a relative sense, but also in an absolute sense. Such paradoxical outcome is generic, for it results from neither ad hoc assumptions on market structure nor on information sets, but from the conventionally granted “convexity” assumption on cost functions. An analogous phenomenon is observed for oligopsony market.

The purpose of this paper is to propose a numerical algorithm able to describe the Stackelberg strategy for a multi level hierarchical three-person game via genetic algorithm (GA) evolution process. There is only one player for each hierarchical level: there is an upper level leader (player L0), an intermediate level leader (player L1) who acts as a follower for L0 and as a leader for the lower level player (player F) that is the sole actual follower of this situation.

The paper presents a computational result via GA approach. The idea of the Stackelberg-GA is to bring together GAs and Stackelberg strategy in order to process a GA to build the Stackelberg strategy. Any player acting as a follower makes his decision at each step of the evolutionary process, playing a simple optimization problem whose solution is supposed to be unique.

A GA procedure to compute the Stackelberg equilibrium of the three-level hierarchical problem is given. An application to a Authority-Provider-User (APU) model in the context of wireless networks is discussed. The algorithm convergence is illustrated by means of some test cases.

The solution to each level of hierarchy is supposed to be unique.

The paper demonstrates the possibility of using computational procedures based on GAs in hierarchical three level decision problems extending previous results obtained in the classical two level case.

This paper aims to present various three-level service contracts among the following three participants: a manufacturer, an agent and a customer. The interaction between the aforementioned participants will be modeled using the game theory approach. Under non-cooperative and cooperative games, the optimal sale price, warranty period and warranty price for the manufacturer and the optimal maintenance cost (repair cost) and marketing expenditure for the agent are obtained by maximizing their profits. The satisfaction of the customer is also maximized by being able to choose one of the suggested options from the manufacturer and the agent, based on the risk parameter.

Three-echelon supply chains with marketing and warranty services are studied. Game-theoretic approaches (non-cooperative and cooperative) are presented. The non-cooperative approaches are static (NE) and dynamic (Stakelberg) models. The cooperative approach is related to bargaining models (Nash bargaining games). The authors develop a sensitivity analysis of some parameters and their effect.

Based on the mentioned drawbacks (i.e. lack of a model containing warranty, marketing and pricing), despite their importance, a developed model is proposed in this research to cover one of the research gaps. In addition, main contributions of this paper that differentiate it from the existing papers are regarding inventory, lost sale and lost goodwill, which are significant in the comparison environment. Another advantage of this study is related to the solution approach, the game theory. Twofold of the games theoretical, i.e. cooperative (in three forms) and non-cooperative are considered, because of their importance. Three types of non-cooperative games are presented as follows: Nash equilibrium – each echelon decides respectively and simultaneously; manufacturer-Stackelberg – the manufacturer has more power than the agent and the agent has more power than the customer; and customer-Stackelberg – customer is leader of the agent and the agent is the leader of manufacturer. The involved cooperative game in this paper is the bargaining problem that the participants can determine how to share the additional profits.

In this paper, various three-level service contracts will be presented among the following three participants: a manufacturer, an agent and a customer. The interaction between the aforementioned participants will be modeled using the game theory approach. Under non-cooperative and cooperative games, the optimal sale price, warranty period and warranty price for the manufacturer and the optimal maintenance cost (repair cost) and marketing expenditure for the agent are obtained by maximizing their profits. The satisfaction of the customer is also maximized by being able to choose one of the suggested options from the manufacturer and the agent, based on the risk parameter. Several numerical examples are used to illustrate the models presented in this paper. Finally, the authors develop a sensitivity analysis of some parameters and their effects on the objective functions.

Aims to analyse the labour market outcome when there are two unions in the industry, representing heterogeneous workers – imperfect substitutes in production.

Competition between union policies are viewed in terms of both employment and wage strategies. Results for substitutes and complements are inspected. Attention is given to the strategic behaviour of the unions, towards one another and/or the employer side. Cooperation is modelled using the Nash‐maximand approach.

Gathers some notes and enlargements to the standard collective bargaining problem in which unions maximise utility. Extends the framework to model union competition behaviour for jobs and/or employment that reproduces the standard market product analysis of imperfect competition. Focuses on heterogeneous labour.

The analysis concentrates on the case of union duopoly, but can easily be enlarged to the n‐union setting – which is left for further investigation.

A simple analytical example with Stone‐Geary union utility functions and a linear labour demand system is forwarded.

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.

The purpose of this paper is to provide a framework to help business marketers with online and traditional retail channels (multi‐channel retailers) to find the optimal branding strategy and market structure in order to maximize their profits.

A game‐theoretic model is developed to determine the optimal branding strategy and market structure for the dual‐channel stores of a multi‐channel retailer.

The paper demonstrates that an optimal branding strategy and market structure exists for the dual‐channel stores of a multi‐channel retailer. When a retailer uses multiple channels in parallel to sell its product, the optimal branding strategy is to employ as large as possible brand differentiation between the dual‐channel stores, particularly when the price is less sensitive for consumers and the market base size is larger. Furthermore, it is also found that the optimal market structure is the Stackelberg mode, especially when the product brands between the two channels are less differentiated.

The present study assumed that all information is known to both the online and traditional channels of a multi‐channel retailer. However, information could be incomplete. It is recommended that future research explore the value of product brand differentiation under incomplete information settings.

The paper provides a very useful model framework, branding strategy, and market structure for business managers who are using or planning to use multiple channels to sell their products.

This paper fills a conceptual and practical gap for a structured analysis of the current state of knowledge about multi‐channel branding strategies. The paper provides practical and solid advice and examples demonstrating the application of product brand differentiation strategies for business managers.