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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.

The problem of manufacturer-customer relationships is becoming the key factor of enterprise development, and the contradiction between manufacturer’s objective and customer’s satisfaction still exists. Customers claim for product safety from manufacturers, so manufacturers should take corporate social responsibility (CSR) into their company philosophy or even enhance the degree of CSR during their production. The purpose of this paper is to investigate the influences of parameters on the stability of risk-averse complementary product manufacturers.

In this study, three dynamic game models are developed: manufacturer 1 – leader Stackelberg game model, manufacturer 2 – leader Stackelberg game model and Nash game model. Using bifurcation diagrams, the largest Lyapunov exponent, 0-1 test for chaos and parameter basin plots, the influences of parameters on the complex behaviors of the three models are analyzed.

The authors demonstrate that the system exists in deterministic chaos when the parameter exceeds a certain value. The lead manufacturer will not be a beneficiary in chaotic state, and when two manufacturers have the same status the stability of the system weakens, which renders it easily chaotic.

In this paper, the authors make some assumptions, which when applied broadly could lead to some findings.

The authors find that the lead manufacturer will derive the greatest profit and will exert the least effort compared with the follower manufacturer, but that both manufacturers will exert greater effort in the Nash game. The two manufacturers should be cautious while selecting the parameter ' s value so that the stability of the system is maintained.

The research will serve as a guide for the two complementary manufacturers in their decision-making process.

The originality and value of the research rest on the use of dynamic thinking in ensuring stability in the quality of complementary products considering the firms’ market powers. The research will serve as a guide for the two complementary manufacturers in their decision-making process.

The purpose of this paper is to propose a portfolio procurement framework to response to uncertain customer demand and purchasing price volatility in a simultaneous manner. Then it aims to obtain optimal procurement and production decisions under the portfolio framework to maximize profit.

The portfolio procurement problem is modeled as a dynamic Stackelberg game and Nash equilibrium solutions are obtained. The portfolio procurement framework is analyzed in the settings, with both risk-neutral objective and downside risk constraints measure of contract prices.

By obtaining the Nash equilibrium solutions for both the buyer’s ordering decisions and the supplier’s optimum production decisions, Stackelberg game model for portfolio procurement is proved to be feasible. Additionally, downside risk constrains are proposed to help supply chain participants’ to evaluate the profitability and risk probabilities of the designed procurement contracts under the uncertain customer demand and spot market.

This paper assumes the supplier is risk averse and the buyer is risk neutral, and it would be interesting to examine the performances of portfolio procurement strategy with different risk attitudes participants.

This research could help the buyer respond to not only demand uncertainty but also the volatile spot price in the procurement process. Related optimal portfolio procurement strategy can be carried out to improve the enterprise’ procurement plan by adjusting the order of long-term contract, option contract and the spot market. The proposed framework could also help suppliers design and evaluate contracts for buyers with different risk preference, and on the other hand help the buyers decide if she should accept the contracts from the supplier.

This research should also increase awareness in both academia and industry on the opportunities of using the dynamic portfolio procurement approach to enhance flexibility and to mitigate the inventory as well as price risks in the procurement process. Effective downside risk constrains on contract prices could also help to protect the bottom line of companies with different risk preference.

The portfolio procurement framework proposed in this research can mitigate inventory and price risks simultaneously. Also, instead of solving the portfolio procurement planning problem in computational simulation experiments as in previous research, this paper proposed a dynamic game model for this portfolio-based procurement problem and obtained its Nash equilibrium solutions for both the buyer’s ordering decisions and the supplier’s optimum production decisions. Finally, an innovative and simple downside risk constraints has been designed to help the buyer evaluate supplier’s contract prices according to their individual risk preference.

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.

The authors consider a dynamic emission-reduction technology investment decision-making problem for an emission-dependent dyadic supply chain consists of a manufacturer and a retailer under subsidy policy for carbon emission reduction. The consumers are assumed to prefer to low-carbon products and formulate a supply chain optimal control problem.

The authors adopt differential game to analyze investment strategies of cost subsidy coefficient with respect to vertical incentive of a manufacturer and a retailer. A comparison analysis under four different decision-making situations, including decentralized decision-making, centralized decision-making, maximizing social welfare, is obtained.

The results show that the economic benefit and environmental pressure have a win–win performance in centralized decision-making. In four different game models, equilibrium strategies, profits and social welfare show changing diversity and have a consistent development trend as time goes on.

The authors estimate the demand function is a linear function in this paper. According to the consumers’ preference to low-carbon products, consumer’s awareness meets the law of diminishing marginal utility like advertising goodwill accumulation. The carbon-sensitive coefficient might be a quadratic expression, which will complicate the problem and be consistent with reality.

It captures that there is a necessity to strengthen cooperation and exchange of carbon emission technology among the enterprises by simulation of different decision-makings when government granted cost subsidy.

The results provide significant guidelines for the supply chain to make decision-makings of emission-reduction technology investment and relevant government departments to determine emission subsidies costs.

An endogenous subsidies coefficient is produced by the social welfare function. Distinguished from previous study, it also considered the influences of carbon emission trade policy and consumer preference.

This paper considers an option contract in a two-stage supplier-retailer supply chain (SC) when market demand is stochastic. The problem is a Stackelberg game with the supplier as a leader. This research assumes demand information sharing. The purpose of this study is to determine the optimal pricing strategy of the supplier along with the optimal order strategy of the retailer in three option contract cases.

The paper model the option contract pricing problem as a bilevel problem. The problem is then solved using bilevel programing methods. After computing, the generated outcomes are compared to a benchmark (wholesale price contract) to evaluate the contract.

The results reveal that only one of the contract cases can arbitrarily allocate the SC profit. In both other cases, the Stackelberg supplier manages to earn the total SC profit. Further analysis of the first contract, show that from the supplier’s perspective, the first stage forecast inaccuracy is beneficial, whereas the demand uncertainty in the second stage is detrimental. This contracting strategy guarantees both players better outcomes compared to the wholesale price contract.

To the best of the authors’ knowledge, this research is the first that links the option contract literature to the bilevel programing literature. It also the first to solve the pricing problem of the commitment option contract with demand update where the retailer exercises the option before knowing the exact demand.

This paper aims to find optimal emission reduction investment strategies for the manufacturer and examine the effects of carbon cap-and-trade policy and uncertain low-carbon preferences on emission reduction investment strategies.

This paper studied a supply chain consisting of one manufacturer and one retailer, in which the manufacturer is responsible for emission reduction investment. The manufacturer has two emission reduction investment strategies: (1) invest in traditional emission reduction technologies only in the production process and (2) increase investment in smart supply chain technologies in the use process. Then, three different Stackelberg game models are developed to explore the benefits of the manufacturer in different cases. Finally, this paper coordinates between the manufacturer and the retailer by developing a revenue-sharing contract.

The manufacturer's optimal emission reduction strategy is dynamic. When consumers' low-carbon preferences are low and the government implements a carbon cap-and-trade policy, the manufacturer can obtain the highest profit by increasing the emission reduction investment in the use process. The carbon cap-and-trade policy can encourage the manufacturer to reduce emissions only when the initial carbon emission is low. The emission reduction, order quantity and the manufacturer's profit increase with the consumers' low-carbon preferences. And the manufacturer can adjust the emission reduction investment according to the emission reduction cost coefficient in two processes.

This paper considers the investment of emission reduction technologies in different processes and provides theoretical guidance for manufacturers to make a low-carbon transformation. Furthermore, the paper provides suggestions for governments to effectively implement carbon cap-and-trade policy.

The purpose of this paper is to describe how the performance of a system is determined.

Systems with the same structure or function often have different performances. What makes the difference? Within a system, the various actors make their decisions by their own and their actions depend on the mechanism of the system. The actors' strategy selection under different mechanisms and the mechanism design are precisely in the range of Game Theory. This paper compares two different pricing mechanisms, the Stackelberg Game and Cournot Game, in a linear supply chain. And the obtained result of the different behavior (Pm*, Pr*) and different performance (Um*, Ur*) of the supply chain obviously approves our proposition that the operational mechanism is of great importance to the performance of the system, the same as structure.

It is the structure of the system and operational mechanism which determines the performance of the system.

The paper's limitations lie in the fact that it is not yet based on experimental evidence from real‐world systems.

Game Theory is one of the most effective methods to study the systematic mechanism, especially the mechanism designs, because it reveals the inherent nature of the systematic mechanism.

This paper points out that the mechanism which restricts each behavioral subject determines the performance of these systems. It puts forward a new region for the research of general system theory.

This paper aims to analyze the impact of the cost coefficient of product emission reduction, coefficient of low-carbon product advertising effort cost, and sharing ratio of low-carbon product advertising effort cost on the profit of a dual-channel supply chain. After determining the best model and relevant influencing factors, the paper puts forward corresponding management inspirations and suggestions.

The paper opts for an exploratory study using Stackelberg game theory to construct a centralized decision-making (MC mode), a low carbon product advertising effort cost free sharing decentralized decision-making (SD model) and a low carbon product advertising effort cost sharing decentralized decision-making (JD model) game model. Through using optimization methods to get the equilibrium solution, the relevant management suggestions are obtained by comparison analysis.

The paper shows that the JD model is better than the SD model in terms of the profits of the manufacturer, retailer and supply chain, and the improvement of Pareto is realized. The proportion of cost sharing of low carbon product advertising effort is positively related to the wholesale price and direct influence coefficient of low carbon product advertising effort on channel, while negatively related to the retail price and the cross influence coefficient of low carbon product advertising effort on alternative channels. Under the JD model, the manufacturer can reduce advertising costs through improving the efficiency and pertinence of direct channel advertising and urging the retailer to do a better job in sales management to improve gross margin and require the retailer to increase advertising efficiency and pertinence of retail channel to reduce advertising costs of retail channel and other ways to increase their profits. The retailer can make use of its advantages closer with consumers to improve the efficiency and pertinence of advertising in the retail channel to raise the influence coefficient of advertising and reduce the advertising cost in the retail channel.

The innovations of this paper are listed as follows: First, it has considered advertising investment from both the manufacturer and the retailer simultaneously. Second, it has considered a low-carbon background to investigate cooperative advertising decision for low-carbon products. Third, it has considered the decision on the level of product emission reduction and the level of low-carbon product advertising effort investment simultaneously.