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In the process of group decision-making, there may be multilayer subjects. In other words, members of the decision-making group may come from different layers and there is interest game among decision experts. Therefore, it is an extremely important topic to aggregate the information of decision experts who are involved in hierarchical relations and gaming relations so as to effectively address game conflicts and reach game cooperation.

First, a programming model is established to minimize the difference of expert opinions in hierarchical decision-making, and the method to solve the optimal solution is given. Second, the cooperative game model and its properties are discussed by using cooperative game and Shapley value, and the method to determine the weight vector between layers is also proposed.

This model can quickly aggregate information and achieve game equilibrium among decision-makers with hierarchical relationships. It can be widely used in decision evaluation with hierarchy structure and has certain practical value.

In order to solve the problem that experts at different levels may have conflicts of interest in multilayer grey situation group decision-making process, cooperative game and Shapley value theory are introduced into the study, and a multilayer grey situation group decision-making model based on cooperative game is constructed. The validity and practicability of the model are illustrated by an example.

The purpose of this paper is to propose a complete theory of grey conflict analysis model based on grey game and the graph model for conflict resolution and also, to illustrate a case of “prisoner's dilemma” in the traditional grey game as an example.

Based on the theories of grey game and graph model for conflict resolution, this paper concentrates on the model of grey conflict analysis in a case of two players under the condition of symmetrical loss information. By analyzing decision makers, strategies, states, graph model and grey potential, and the number of decision makers' steps, the pure strategy Nash equilibrium is extended to grey potential‐general metarationality, grey potential‐symmetrical metarationality, and grey potential‐sequential stability. Meanwhile, the logical relationships between solutions are discussed. A specific case study is carried out to illustrate how the proposed grey conflict analysis model is used in practice.

The results in this paper indicate that more stable solutions are found when one considers the grey potential‐general metarationality, the grey potential‐symmetrical metarationality, and the grey potential‐sequential stability, and then solve the paradox of “prisoner's dilemma”.

This new grey conflict analysis model could be used to provide useful information for policy makers during existing conflicts or negotiations among parties or enterprises.

The paper succeeds in constructing a new grey conflict analysis model, in which the solution concepts are studied; and the two‐player grey game will be extended to n‐players in the near future.

The purpose of this paper is to extend the results of Meca et al. (2004) depending on the grey information revealed by the individual firms.

The authors introduce cooperative grey games and focus on sharing ordering cost rule (SOC-rule) to distribute the joint cost.

In this study, the authors introduce a model, where inventory costs are assumed as grey numbers instead of crisp or stochastic ones studied in literature. At first, grey numbers and classical cooperative inventory games are recalled. Then, cooperative grey games are introduced and related results are given. Finally, an application is performed for three shotgun companies in Turkey.

It is an effective approach for theoretical analysis of systems with imprecise information and incomplete samples. Therefore, grey system theory, rather than the traditional probability theory and fuzzy set theory, is better suited to model the inventory problems by using cooperative game theory. To the best of the knowledge no study exists modeling inventory situations by using cooperative grey games. From this point of view this study is a pioneering work on a promising topic.

The purpose of this paper is to attempt the construct of a Centipede Game network model of investment in real estate market based on grey integration and forwards induction.

The investment process of decision making in the real estate market is a multi-agent-stage dynamic process. The behavior of the game are interdependent and the ultimated equilibrium is an outcome of every the game adjust themselves comprehensively in certain conditions. The paper constructs a Centipede Game network model of investment in real estate market based on grey integration and forwards induction, regulars the method framework based on grey integration and forwards induction.

The results verifies that the validity of Centipede Game network model by taking N's real estate market as an example.

Most of the existing real estate market game researches study it from the view of pairwise game or one-to-many game, in fact, the game tend to be developed in the form of a network. And the paper puts forward Centipede Game network model based on the mode of players game in real estate market.

The paper succeeds in providing a new and systematic framework of studying the real estate market game by using game theory.

One important assumption in the conventional cooperative game theory is that payoffs are assumed to be deterministic. In terms of the players’ cognitive ability of the realistic world, this is a very strict assumption. The classical game theory can find no way out when a particular game circumstance involves uncertainty, such as limited knowledge, small sample, and inadequate information, the payoff values of the game can only be described with interval grey numbers. The paper aims to discuss these issues.

In this study the concept of N-person grey games is proposed in which payoffs are represented with interval grey numbers opposed to the classical game theory. A straight forward solution methodology is submitted compatible to grey numbers. Then, a currency war between anonymous countries is handled and modeled as an N-Person grey game. A generic currency war scenario is developed to follow the proposed solution procedure thoroughly.

Based on the outcomes of this work, the authors can say that N-person grey game is an expansion of the classical N-person game under uncertain grey information and can be applied in more complex and uncertain environments, such as those seen in complicated currency warfare.

This study combines the grey system theory with the classic N-person game theory and sets up the N-person grey game with grey payoff functions. Based on the grey number operating methods, the grey linear programming algorithm is established to calculate and distribute benefits to the players. In this respect this study has the feature of being the pioneer in the N-person grey game area.

The improved classical model makes it possible that the evaluation strategy has an optimal tendency, which reveals the purpose of this paper is to facilitate the first price sealed-bid auction more in line with the actual situation. To be more specific, there are several merits in the improvement process. On the one hand, the bid-winning probability can be improved for the bidder; on the other hand, the real market value of the subject matter can be more clearly recognized for the employer.

Bayesian estimation and grey system theory are referenced in this paper, with the use of double-parameter estimation, little historical data and expert experience. Specific implementation steps are as follows: first of all, using the double-parameter Bayesian estimation to correct the actual valuation of the bid matter v, then introducing the threat factor grey number R in the auction model, giving the improving of the optimal grey quotation and grey expectation utility under the two-party game and finally taking the aerospace component procurement as an example, simulating the bidding process of the bidding parties to arrive at the optimal bid strategy.

The improved model shows that the optimal strategy will change with the threat factor rather than a fixed value. When the threat factor grey number R follows [0.4, 0.6], the optimal quotation strategy will appear, which means quotation is higher than 50% of the bid matter's valuation.

The improved model proposed in this paper can strengthen the cost control in the Chinese commercial space process and optimize the pricing strategy for the final launch.

The modified model changes the habit that the bidder's valuation of the bid subject to mainly come from experience and to prompt the model for making full use of little historical data on the foundation of the former. It can reduce the subjective judgment error in the game results; finally, the practical cases are simulated in MATLAB at the same time, and the simulation effect is good, so we can get some more realistic conclusions on this basis.

The purpose of this paper is to summarize the progress in grey system research during 2000-2015, so as to present some important new concepts, models, methods and a new framework of grey system theory.

The new thinking, new models and new methods of grey system theory and their applications are presented in this paper. It includes algorithm rules of grey numbers based on the “kernel” and the degree of greyness of grey numbers, the concept of general grey numbers, the synthesis axiom of degree of greyness of grey numbers and their operations; the general form of buffer operators of grey sequence operators; the four basic models of grey model GM(1,1), such as even GM, original difference GM, even difference GM, discrete GM and the suitable sequence type of each basic model, and suitable range of most used grey forecasting models; the similarity degree of grey incidences, the closeness degree of grey incidences and the three-dimensional absolute degree of grey incidence of grey incidence analysis models; the grey cluster model based on center-point and end-point mixed triangular whitenization functions; the multi-attribute intelligent grey target decision model, the two stages decision model with grey synthetic measure of grey decision models; grey game models, grey input-output models of grey combined models; and the problems of robust stability for grey stochastic time-delay systems of neutral type, distributed-delay type and neutral distributed-delay type of grey control, etc. And the new framework of grey system theory is given as well.

The problems which remain for further studying are discussed at the end of each section. The reader could know the general picture of research and developing trend of grey system theory from this paper.

A lot of successful practical applications of the new models to solve various problems have been found in many different areas of natural science, social science and engineering, including spaceflight, civil aviation, information, metallurgy, machinery, petroleum, chemical industry, electrical power, electronics, light industries, energy resources, transportation, medicine, health, agriculture, forestry, geography, hydrology, seismology, meteorology, environment protection, architecture, behavioral science, management science, law, education, military science, etc. These practical applications have brought forward definite and noticeable social and economic benefits. It demonstrates a wide range of applicability of grey system theory, especially in the situation where the available information is incomplete and the collected data are inaccurate.

The reader is given a general picture of grey systems theory as a new model system and a new framework for studying problems where partial information is known; especially for uncertain systems with few data points and poor information. The problems remaining for further studying are identified at the end of each section.

The purpose of this paper is to analyze the market share of two competing enterprises from the perspective of consumer preferences on both of their products. For different industrial types, this paper discusses how domestic firms make decisions to compete with the multinational company based on consumer’s preferences on different types of products from different companies.

Considering the different types of equipment manufacturing industries, consumers’ differentiated preferences for Chinese domestic equipment manufacturers and multinational equipment manufacturers, as well as the uncertainty of technological level and dependence on production factor in reality, this paper introduces the interval grey number into the Stackelberg game model and analyzes the market share of two competing enterprises and the consumer preferences for both of their products based on different industrial types.

The results show that when both of the two competing firms are engaged in R&D activities, consumers prefer domestic products, and with the improvement of technological level, this preference grows stronger, but the market share of the multinational enterprise is higher than that of the local enterprises. When the two competing enterprises are engaged in manufacturing activities, consumers are more inclined to choose products of the multinational company, and with the increasing dependence on production factors, the preference becomes stronger. Meanwhile, the market share of the multinational company is higher than the local enterprise. Therefore, from the perspective of consumer preference, China’s domestic equipment manufacturing enterprises should choose technology-intensive or technology and labor-intensive industries (or dual-intensive industries).

In the context of international competition, from the perspective of consumer preference, the research on industrial selection is relatively rare, and does not take into account the influence of the uncertain influence brought by technological-level and production factor dependency. Therefore, this paper analyzes the influence of technological-level and production factor dependency on consumer preference among various types of industries. Based on the concept of consumer preference, and combining with the interval grey number, the improved grey game model is constructed to analyze the influence of the uncertainty of enterprise’s technological-level and production factor dependency on the market share of two competing companies, finally coming up with the direction into which the Chinese equipment manufacturing industries should develop.

In order to more accurately predict the dynamics of the e-commerce market and increase the comprehensive value of the circular e-commerce industry, proposes to use Grey system theory to analyze the circular economy of the e-commerce market.

Construct a Grey system theory model, analyze the big data of e-commerce and circular economy of the e-commerce market and predict the development potential of China's e-commerce market.

The results show that the Grey system theory model can play an important role in the data analysis of circular economy of the e-commerce market.

Use Grey model to analyze e-commerce data, discover e-commerce market rules and problems and then optimize e-commerce market.

The purpose of this paper is to summarize the advances in grey system theory research and various application achievements in science and engineering. At the same time, it commemorates the 40th anniversary of the birth of grey system theory and the 10th anniversary of Grey Systems–Theory and Application.

Firstly, the innovations of theoretical research in grey system theory were summarized and some of the widely recognized new results are briefly described. By searching and combing the research results of grey system theory in China national knowledge infrastructure (CNKI) database and Web of Science by Institute for Scientific Information (ISI), this paper shows the rapid development trend of grey system theory in the past 40 years, and the successful applications of grey system theory in the fields of social sciences, natural sciences and engineering technologies.

More than 227 thousands literature were found by input 10 phrases such as grey system, grey number and sequence operator etc. in CNKI database. After entering the new century, the number of grey system papers included in CNKI database is increasing rapidly. Since 2008, more than 10 thousands papers have been included per year and more than 15 thousands papers have been included per year since 2014. Grey system method and model are widely used in physics, chemistry, biology and other fields of natural science, as well as transportation, electric power, machinery and other fields of engineering technology, and a large number of valuable results have been achieved.

It can be seen that the grey system theory plays an important role in promoting China’s scientific and technological progress, innovation and development and high-level talent training from tens of thousands of literatures marked with important national science and technology projects and a large number of grey system literatures published by China’s double first-class universities and double first-class discipline construction universities.

Both innovations of theoretical research and practical application play important role in the growth of new theory. The innovations of theoretical research provide methods and tools for practical application, which is conducive to improve application efficiency and broaden application fields. A large number of practical applications needs have become the source of theoretical innovation and the solid background for the birth of theoretical innovation achievements.