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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.

Goes back to thinking on the price theory of oligopoly in 1960. In particular, is concerned with Stackelberg’s oligopoly theory. Presents a careful description of the development of Stackelberg’s analysis. Takes into account his mathematical appendix. Confronts the theory with game theory and concludes that in a dynamic game a Nash‐Cournot equilibrium will emerge.

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.

An apparel supply chain primarily consists of geographically distant suppliers, manufacturers and retailers. The coordination among the members of the supply chain becomes difficult when we consider the triple bottom line of sustainability in it. Moreover, the complexity increases with the change in dominance power of the respective members. However, the task of managing the channel further becomes complicated after incorporating sustainability and dominance power simultaneously into the supply chain. To fill this gap, this paper focuses on designing of mechanism and demonstration of three-echelon model to coordinate sustainable supply chain.

In this paper, the noncooperative game theoretic method has been applied for the exploration of models. The various structures of the centralized and decentralized supply chain are considered on the basis of a player's dominance power. The model uses simultaneous and sequential move games to analyze optimal profit of supply chain agents, total channel profit, green innovation level and corporate social innovation level.

Analytical results show that simultaneous game performs better than the sequential game. The consumer sensitivity toward green and social innovations increases total channel profit. We also proposed a linear two-part tariff contract model. The proposed model enhances the sustainability level and leads to perfect channel coordination. Using a numerical example, we present the effectiveness of multiple game structures under centralized and decentralized settings. The results reveal that channel efficiency is the highest in the two-part tariff contract followed by a simultaneous move game structure and lower in the cases of sequential move game.

In this research, model setting are deterministic and there is no any information asymmetry. Therefore researchers are encouraged to study multiechelon sustainable supply chain coordination models under stochastic and information asymmetry settings.

The paper includes implications for the development of sustainable supply chain coordination model to tackle the problems of dominance power, sustainability issues and lower channel efficiency of supply chain.

This study proposes game-theory-based three-echelon sustainable supply chain for the channel coordination.

This paper aims to consider the problem of determining the equilibriums on oligopoly market in case of Stackelberg leader (leaders) and reflexive behavior of market agents.

This paper includes economic and mathematical modeling, optimization methods and game theory.

This paper explains models of reflexive games on oligopoly market, taking into account the diversity of agents’ reasoning about strategies of environing and equilibrium mechanisms for coincidence or opposition of agents’ reflexive reasoning on the same rank of reflection.

This paper considers the oligopoly market with linear function of demand and costs of agents, the rational behavior of agents and the reflexive reasoning on the same rank of reflection. The set of agents’ reasoning about the environing strategies is considered as a set of market states for which the problem of agent’s optimal action choosing solves with the complete awareness.

Identification of reflexive behavior of environing allows agents to increase their market shares and profit.

Oligopoly markets play a leading role in the world oil trade and reflexive behavior affects the market equilibrium.

In the paper, the mechanisms of equilibrium in reflexive games on the linear duopoly market for arbitrary rank reflection are developed.

Most pricing studies assume that firms have complete information about demand. In practice, managers must make decisions, given incomplete information about the demand for their own products as well as those of their rivals. This paper develops a duopoly pricing model in which firms market differentiated products in a world of uncertainty. Results show that the predictions of standard strategic pricing models may not hold when firms face parameter uncertainty and are risk‐averse. Under well‐defined conditions, there may be a “first‐mover” disadvantage to the firm that attempts to be the Stackelberg price leader in the market, especially in a market where demand is highly uncertain. Interestingly, if parameter uncertainty is sufficiently high, it may even be necessary for the price leader to share market information with its rival. When firms are risk‐averse, uncertainty generally decreases equilibrium prices and the variabilities of profits.

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.

The purpose of this paper is to investigate optimal decision methods under a cooperative situation in two-echelon logistic models.

The authors propose the optimal strategies of exporters in the three types of rival game behaviors: Stackelberg, Collusion, and Cournot, each of which provides the optimal decision for the duopolistic shippers and the oligopolistic forwarders in each scenario.

From the empirical studies the paper finds that among three scenarios, the oligopolistic treatment of forwarders’ actions demonstrates that Stackelberg behavior can carry out the maximum profit, and Collusion game can achieve the maximum profit for the shippers.

Proposed an optimal decision methods in two-echelon logistic models.

This paper aims to study the impact of existence and lack of discount on the relationships between one manufacturer and one retailer under the cooperative and the non-cooperative games and the members’ profits are compared.

In the first approach, the manufacturer’s price function is constant, and in the second approach, this price function is a decreasing function with respect to lot size. These approaches are modeled through three games structure, including two Stackelberg games and one cooperative game.

Some numerical instances comprising sensitivity analysis are provided, and then the members’ profits in different scenarios are compared. This paper reveals that in the presented models, whether the members are inclined to change their profits.

This paper presents a tool of decision-making for the type of relationships of members in two different circumstances, and an approach is also presented to maximize the members’ profit.

In this paper, the relationships between one manufacturer and one retailer are studied under six different circumstances, where pricing, cooperative advertising and inventory cost are considered simultaneously. Also, a different model is presented to make a balance in individual profits and gain more profit for each member compared to the cooperative and non-cooperative game.