| The origin of the differential games theory might trace in the 1940s. In 1965, Isaacs wrote the classics work "Differential Game". Afterward Bellman (1957) finished "Dynamic programming" and Pontryagin (1962) completed "The Mathematical Theory of Optimal Process". The three works became the foundation of the deterministic differential games theory. As time goes by, more scholars started to pay attention and in-depth study of differential game, with unremitting efforts to promote the advanced form of game theory to evolution, challenging the hierarchy of application of mathematical theory, the classical theory at the bottom of the conventions.For nearly three decades, the game theory has formed a complete theoretical system, the game theory ideas and methods are also becoming critical analysis of mainstream economics paradigm, its scope of application covers the entire field of economics, and gradually to sociology, biology, physics and other social sciences and natural sciences to expand. Important characteristic of today's economy and society is a highly specialized production and operation of collaborative, from confrontation to cooperation, from competition to collaboration has become the consensus of the various economic entities as large as sovereign states and international economic cooperation organizations, small to micro firms, or economic entity, have attached great importance to cooperation and coordinated development. Many of the economic cooperation of the analysis and interpretation are based on cooperative game theory foundations. However, the reality of the economic cooperation is not as a static cooperative game model characterization and interpretation of the same, due to the passage of time progress and economic decision-making of the main changes in the environment, under the framework of the optimal static equilibrium may no longer apply, can not guarantee that the economic co-operation carried out smoothly. Cooperative differential game theory can solve this problem an effective way. Cooperative differential game can be understood as a continuous time dimension, by the unlimited choice of strategy, the pursuit of the overall rationality and individual rationality of cooperation made by the participants, It can directly influence the behavior of all other participants in interaction. Cooperative games theory can be thought as the instantaneously mutual behavior of the players whose objects are group rational and individual rational which can affect the other players in continuous time.Static cooperative games require the existence of cooperative agreement with sanction, and explicit whole payoffs allocation plan, which emphasizes to satisfy under overall rationality fair and efficiency. After time factor is introduced into static state cooperation games, the binding force agreement prerequisite might relax in the static environment. The reason is dynamic game itself requests its balanced solution to satisfy time consistency, namely sub-game uniformity. This means that at first determined-together agreement binding force will be in biochemistry, the balanced solution which will assign by the initial agreement will probably satisfy the time consistency, its binding force condition and the time consistency will request to combine into one. The article calls at-first agreement the most superior criterion, it achieves projects and so on agreement including the maximized joint return and on the income distribution. From this, a cooperation differential game balanced solution must satisfy the time consistency guaranteeing that all participants along the most superior state point locus, according to the most superior criterion allocation plan which at first formulates together, cooperates continually, each time does not have the deviation, ended until the cooperation. The article here only proposes an assignment that takes the cooperation differential game balanced solution the necessary and sufficient condition must formulate one kind to be able to guarantee and realize this allocation plan mechanism, thus the guarantee cooperation will carry on smoothly.The article topic is "Research on Relevant Issues of Cooperation Differential Games" which is for the purpose of conducts the deep research after the cooperation differential games theory, formulates one kind to satisfy the time consistency, and can guarantee that under the most superior criterion the allocation plan can continue the effective payoffs distribution mechanism, proposed that several spots have the value suggestion. And applies this kind of mechanism in the practice, the analysis and the explanation economic phenomena, the processing economic problem, will cooperate the differential games theory and the reality economic activity close relation.First, from the time point of view of continuity and strategy defines an infinite differential game, and on this basis differential game proved the existence of Nash equilibrium. Cooperative differential game is given structure and meaning of its basic elements of economics has done deeply analysis and interpretation. And discussed a total of state variables, the Hamilton function and transversality conditions for economic interpretation. At the same time gives the non-cooperative differential game equilibrium solution of the time consistency of guidelines, based on co-operation is also given the time differential game equilibrium solution consistency criteria, namely the time to ensure consistency in implementation of the cooperative game, the overall rationality and individual rationality have been maintained, and the optimal state trajectory along the game, in the current distribution of cooperative games starting the program, even if applied to the subsequent start of the cooperative game, still the best. However, the success of co-operation not only requires a balanced solution of the time of its consistency, it also requires must be able to ensure consistency mechanism to safeguard this time.The article uses the cooperation differential games balanced solution's time uniform criterion, proposed has "equilibrating instant payoffs" "payoffs distribution mechanism", is for the purpose of using this kind of mechanism, guaranted at first formulates together under the most superior criterion's balanced allocation plan satisfies the time consistency, and continues effectively, thus guaranteed that the cooperation carries on smoothly. The payoff distribution mechanism is realizes gambles the allocation plan guarantee which each cooperation participation side approval and approves continually locks at first. From the mechanism produces the assignment is in the entire games period, lights in each time, satisfies the overall rationality and the individual rational, and for time consistency assignment. But regarding "the distribution" the behavior understanding, may the stratification plane raise "the nature" from "the alliance" altitude. The cooperation whole payoffs's assignment main body is some sub-alliance by no means that even may say, is total alliance by no means. Because the alliance value is creates at times, similarly, the payoffs is also assigns at times. This is likely "the nature" in games each time, compiles the creation from alliance all members place value at the same time, instantaneous distributes it in the alliance member's hand, certainly, "the nature" the distribution motion's criterion namely for at the first optimized criterion which locks together by all alliance participant, "nature" the distribution behavior, it constructs based on the optimized criterion which decides, is dynamic steady. Summed up the payment distribution mechanisms and Yeung and Petrosyan (2005) for the stochastic differential co-designed by the four-point difference in the distribution process, that is basically different ways of thinking, research framework and the use of technology differences, the optimal end point for the handling of payments and the conclusions are different different test.The payoffs distribution mechanism is balanced recompenses with by the instant the most superior end point payoffs constitution, the research obtains, may realize the instant which the time consistency assignment's payoffs distribution mechanism has to be balanced recompenses with the most superior end point payoffs, must satisfy:(1)Along most superior path's each point in time, the participant recompenses the sum total to be equal to both sides when the use is most superior cooperates the strategy instantaneous payoffs sum total; (2) the participant the instant which obtains in the random time sector is balanced recompenses the sum total the current value and its end point payoffs sum of current value, much more than in non-cooperation situation value function; (3) along games most superior path, participant, in the random point in time starts in games obtains the payoffs was equal to, it starts afterward in some time spot in another games obtains payoffs current value, in addition it the current value which between current games with afterward gambled receives all instants which is balanced recompenses. But the most superior condition is equal to the condition in two extremely close time change progress the instantaneous change.For the better understanding instant is balanced recompenses, the article in two people cooperate under the frame has analyzed its intrinsic meaning. The cooperation participant the instant which obtains in the random point in time is balanced recompenses is three sum totals:At first, according to the most superior criterion which formulates, the participant the boundary part which obtains from the whole cooperation payoffs; At first second, according to the most superior criterion which formulates, the participant the boundary part which obtains from the following two items:The first item for its own non-cooperation payoffs; The second item to the time most superior condition's dynamic system transfer at this time by the non-cooperation way to when cooperates the way, to its non-cooperation payoffs instantaneous influence; At first third, according to the most superior criterion which formulates, the participant the boundary part which obtains from the following two items. The first item for the match participant's non-cooperation payoffs's boundary part, the second item to at that time the most superior condition's dynamic system transfer by the non-cooperation way to when cooperates the way, to match participant non-cooperation payoffs instantaneous influence.The article had considered the payoffs cannot shift in the situation the overall rationality, gave in general non-raised games Pareto to be most superior the balanced existence sufficient condition and the essential condition:The proposition have given a Pareto solution essential condition, its direct result is, in two people gamble in the situation, the Pareto boundary may broad regard as a decreasing function; Has given Pareto's effective sufficient condition, simultaneously, has given under the controlled condition, the essential condition is also the sufficient condition.The article has studied in the cross time dynamic environment time consistency and meets one's satisfaction the nature, in a kind of linear conditions differential games, the proving time consistency and meets one's satisfaction the condition. The theorem have proven, if the condition increases a unit, then participant's individual payoffs increases quantity, regardless in cooperates in the situation in the non-cooperation situation, is the same; If adopts the approaches to cooperation in the games preliminary stage to satisfy the individual rationally, will then cooperate has been the individual rational. The proposition had proven if the cooperation solution is the time uniform, then it also to be glad acceptsThe article reveals the assignment which in the technical alliance the member profits has been affects the technical alliance normal operation and the steady progression key aspect, through establishes two cooperation differential games model, studies separately has two participants and many participant's technical alliances. In view of two person of technical alliance question, designs a set of payoffs distribution mechanism, causes Nash to assign the criterion to be able balanced to maintain, guaranteed that achieves a tendency steady corporate plan; In view of three person of technical alliance question, has planned one kind the payoffs distribution mechanism which has the instant to be balanced recompenses, causes dynamic Sharpley to be worth by carrying out, guaranteed that tripartite achieves the time correlation the cooperation plan.The article achievement may induce three spots. First, has defined differential gambling from the time continuity and the strategy infinity angle. Second, in hold under the massive related literature material premise, the fining leaves the article key research content, namely time uniformity and payment distribution mechanism design. The introduction "the payoffs distribution mechanism" and "equilibrating instant payoffs" the concept, takes it as guaranteed that the cooperation most superior criterion continues to follow, the corporate plan continues effectively from beginning to end the mechanism, the mechanism gives from the cooperation differential gambling assignment solution satisfies the time uniformity. Third, constructed the technical alliance cooperation differential gambling model, the design has been able to realize the time uniformity assignment payment distribution mechanism; And carries on the simulation analysis through the Matlab procedure, has confirmed the conclusion rationality.
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