Research On Coalition Formation And Stability Of Cooperative Games And Their Application

Classical cooperative game theory, as an important theoretical branch of game theory, has aroused more and more concern in recent years for it can deal with many cooperative phenomena in the real life. There are mainly two important parts in the classical cooperative games: 1) How to form a coalition; 2) how to allocate the profit effectively after a coalition is formed. Now, many important theoretical results of the above two parts have achieved successful applications in many areas, such as economy, politics and so on.Enterprise strategic alliance is a new, win-win economic organization. Each enterprise tries to participate an effective coalition and to maximize his profits after their cooperation. Thus, an imperfect coalition formation method and an unreasonable profit allocation scheme are the two important factors leading to the conflict phenomenna in an enterprise strategic alliance. Even sometimes a coalition can not be formed or a coalition is disbanded quickly. Compared with the cooperative game theory, it is easily to be found that the formation mode of enterprise strategic alliance is the same as the coalition formation problem in the cooperative game and the profit allocation problem is equal to the solution searching problem in the cooperative game. Therefore, the development of cooperative game theory provides a sounded basis for the research of enterprise strategic alliance.Firstly, in the process of coalition formation, many subjective factors may lead to this process extremely complex. Sometimes, it is difficult to quantify these subjective factors, which directly affecting the stability and the sustainable development of the coalition. Secondly, in the aspect of profit allocation problem, it is another important factor affecting the stability of an alliance, due to some complex problems of uncertainty and some other external factors, usually the profit of an alliance can not be represented by precise numbers. These uncertainties directly influence our correct decision-making in the in real life. So the classical cooperative games theory has some limitations in dealing with the above two circumstances, and the results in classical cooperative game have some restrictions in practice applications. Thus a more effective alliance formation method and a more reasonable profit allocation model are urgently required.Based on the above two considerations, this dissertation focues on the cooperative game theory by using fuzzy mathematics, rough sets, operational research and other related knowledge. This dissertation aims to give some effective coalition formation methods and to discuss some profit allocation solutions in an uncertain environment. The main work in this dissertation can be concluded as follows:1) A matching order-based coalition formation decision-making methodThis dissertation analyzes various factors affecting the formation of a coalition such as emotion factors, reality factors and so on. Firstly by giving a set of subjective preference scale value between players in their selection process, the psychological preference factors are quantitatively expressed, then by giving a profit function between players, some realistic factors are quantitatively expressed, combined with the influence of various factors, a matching sequence function is built for players to select an appropriate partner, some new concepts such as matching unite, priority matching unite, direct interaction matching are defined, two important theorems are proposed to prove that a coalition is formed inevitability under special circumstances. After that some algorithm steps and a flow chart are given. Finally, by a concrete example of enterprise strategic alliance, the effectiveness of this method is verified.2) A rough programming model-based coalition formation decision-making methodThis dissertation firstly analyzes various factors affecting the stability of a coalition in its formation process, some weight indexes of these factors are given by the order relation G1 method, then the weight indexes are screened and revised by clustering analysis method based on similarity. And then we choose the highest alliance stability as the goal, using-maximal compatible classes to simulate the relationship between each enterprise in the coalition, we construct a-maximal compatible classes-based rough programming model using the properties and characteristics of rough planning model. Finally, we analyze the characteristics and effectiveness of our model combining a concrete example of enterprise strategic alliance.3) Solutions for cooperative games with interval payoffsIn this dissertation, the existing solutions for interval cooperative games are firstly analyzed and then they are divided into two major categories: real-value solutions and interval-valued solutions. For real-valued solutions, the advantages and disadvantages of them are firstly discussed and then a real-valued solution called selection core is further researched. The concepts of weak balanced interval cooperative games and minimal weak balanced interval cooperative games are proposed, a necessary and sufficient condition which guarantees a nonempty selection core is proved, furthermore, the inequalities can be simplified on the condition that the left endpoints of interval numbers satisfy the superadditivity. Then we analyze the whole solution space of selection core and the solution λλmethod of selection core is converted into the method solving a linear programming problem. After that the concept of selection dominance core is put forward and the equivalent condition between selection core and selection dominance core are proved. For interval-valued solutions, two kinds ranking methods of interval numbers which have total order are firstly defined, then their features are discussed, after that some interval definitions are gotten, such as interval core, interval dominance core, interval stable set and so on. Some theorems are given to give the relations among these interval solutions.4) Solutions for cooperative games with special interval payoffsBased on 3), this dissertation mainly discusses two kinds of interval cooperative games with special payoffs. Firstly, on the condition that the payoff value of any coalition is not fully used to allocate, a generalized interval cooperative game and its solution concepts, such as generalized interval core, generalized interval dominance core are proposed. Further more, some extended theorems are given to discuss the existence and the relations about its solution concepts. Secondly, on the condition that there is a veto player in a coalition, a big boss interval cooperative game is defined, then a solution called value is given, the featues of these two interval cooperative games with special payoffs are discussed by concrete examples.5) Solutions for cooperative games with fuzzy payoffsThis dissertation focuses on the solutions for cooperative games with fuzzy payoffs. Firstly the existing fuzzy solutions, such as M-core, M-shapely value, H-shapely value are analyzed, then by the interval ranking method based on synthetic effect function defined in 3), a fuzzy number ranking method is proposed, then some fuzzy concepts, such as fuzzy core, fuzzy dominance core are given, then a theorem is proven to show the relation between the fuzzy core and the fuzzy dominance core. τ-...