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1.
In cooperative games over time with uncertainty, a stringent condition (subgame consistency) is required for a dynamically
stable solution. In particular, a cooperative solution is subgame consistent if an extension of the solution policy to a situation
with a later starting time and any feasible state brought about by prior optimal behavior would remain optimal. This paper
derives an analytically tractable payoff distribution procedure leading to the realization of subgame consistent solutions
in cooperative stochastic dynamic games. This is the first time that subgame consistent solutions in discrete-time dynamic
games under uncertainty are provided. 相似文献
2.
Subgame consistency is a fundamental element in the solution of cooperative stochastic differential games. In particular, it ensures that: (i) the extension of the solution policy to a later starting time and to any possible state brought about by the prior optimal behavior of the players would remain optimal; (ii) all players do not have incentive to deviate from the initial plan. In this paper, we develop a mechanism for the derivation of the payoff distribution procedures of subgame consistent solutions in stochastic differential games with transferable payoffs. The payoff distribution procedure of the subgame consistent solution can be identified analytically under different optimality principles. Demonstration of the use of the technique for specific optimality principles is shown with an explicitly solvable game. For the first time, analytically tractable solutions of cooperative stochastic differential games with subgame consistency are derived. 相似文献
3.
Subgame consistency is a fundamental element in the solution of cooperative stochastic differential games. In particular, it ensures that the extension of the solution policy to a later starting time and any possible state brought about by the prior optimal behavior of the players would remain optimal. Recently, mechanisms for the derivation of subgame consistent solutions in stochastic cooperative differential games with transferable payoffs have been found. In this paper, subgame consistent solutions are derived for a class of cooperative stochastic differential games with nontransferable payoffs. The previously intractable subgame consistent solution for games with nontransferable payoffs is rendered tractable.This research was supported by the Research Grant Council of Hong Kong, Grant HKBU2056/99H and by Hong Kong Baptist University, Grant FRG/02-03/II16.Communicated by G. Leitmann 相似文献
4.
Judith Timmer 《Mathematical Methods of Operations Research》2006,64(1):95-106
This paper introduces and studies the compromise value for cooperative games with random payoffs, that is, for cooperative games where the payoff to a coalition of players is a random variable. This value is a compromise between utopia payoffs and minimal rights and its definition is based on the compromise value for NTU games and the τ-value for TU games. It is shown that the nonempty core of a cooperative game with random payoffs is bounded by the utopia payoffs and the minimal rights. Consequently, for such games the compromise value exists. Further, we show that the compromise value of a cooperative game with random payoffs coincides with the τ-value of a related TU game if the players have a certain type of preferences. Finally, the compromise value and the marginal value, which is defined as the average of the marginal vectors, coincide on the class of two-person games. This results in a characterization of the compromise value for two-person games.I thank Peter Borm, Ruud Hendrickx and two anonymous referees for their valuable comments. 相似文献
5.
In theory, a Markov perfect equilibrium of an infinite-horizon nonstationary dynamic game requires from the players the ability to forecast an infinite amount of data. In this paper, we prove that early strategic decisions are decoupled effectively from the tail game in nonstationary dynamic games with discounting and uniformly bounded rewards. This decoupling is formalized by the notion of a forecast horizon. In words, the first-period equilibrium strategies are invariant with respect to changes in the game parameters for periods beyond the forecast horizon. We illustrate our results in the context of dynamic games of exploitation of a common pool resource and make use of the rather natural monotonicity properties of finite-horizon equilibria. 相似文献
6.
拟阵上合作对策的单调解 总被引:2,自引:0,他引:2
本文主要介绍了拟阵上的合作对策Shapley解的结构,并利用强单调性、交换性、概率有效性等三条公理刻画了拟阵上合作对策Shapley解的唯-性.同时讨论了本文的三条公理与Bilbao等人的四条 公理的等价性.最后给出拟阵上合作对策核心的定义及其结构. 相似文献
7.
This article studies the theory of discrete-time backward stochastic differential equations (also called BSDEs) with a random terminal time, which is not a stopping time. We follow Cohen and Elliott [2] and consider a reference filtration generated by a general discrete-time finite-state process. The martingale representation theorem for essentially bounded martingales under progressively enlarged filtration is established. Then we prove the existence and uniqueness theorem of BSDEs under enlarged filtration using some weak assumptions of the driver. We also present conditions for a comparison theorem. Applications to nonlinear expectations and optimal design of dynamic default risk are explored. 相似文献
8.
Zhiyong Yu 《Applied Mathematics and Optimization》2013,68(3):333-359
This paper examines the continuous-time mean-variance optimal portfolio selection problem with random market parameters and random time horizon. Treating this problem as a linearly constrained stochastic linear-quadratic optimal control problem, I explicitly derive the efficient portfolios and efficient frontier in closed forms based on the solutions of two backward stochastic differential equations. Some related issues such as a minimum variance portfolio and a mutual fund theorem are also addressed. All the results are markedly different from those in the problem with deterministic exit time. A key part of my analysis involves proving the global solvability of a stochastic Riccati equation, which is interesting in its own right. 相似文献
9.
We consider integrals of random mappings with respect to consistent random measures in C([0; 1]). 相似文献
10.
D. W. K. Yeung 《Journal of Optimization Theory and Applications》2007,132(1):143-160
This paper presents a cooperative differential game of transboundary industrial pollution. A noted feature of the game model
is that the industrial sectors remain competitive among themselves while the governments cooperate in pollution abatement.
It is the first time that time consistent solutions are derived in a cooperative differential game on pollution control with
industries and governments being separate entities. A stochastic version of the model is presented and a subgame-consistent
cooperative solution is provided. This is the first study of pollution management in a stochastic differential game framework.
This research was supported by the Research Grant Council of Hong Kong Grant HKBU2103/04H and Hong Kong Baptist University
Grant FRG/05-06/II22. 相似文献
11.
12.
Mathematical Notes - It is well known that, for cooperative games with transferable utility (and with crisp payoffs), the set of reasonable imputations is nonempty. It is also known for what values... 相似文献
13.
E. V. Shevkoplyas 《Journal of Mathematical Sciences》2014,199(6):715-722
We study optimal solutions in differential games with random duration. 相似文献
14.
In this article, we consider a problem in games of chance. Our result shows that two losing games ( A and B , in the sense of a negative expectation) can become a winning game (in the sense of a positive expectation), when the two are played in a suitable alternating order; for example, ABBABB ....... By using a regrouping technique in Automata and the concept of Markov chain embedding, we give proof of this gambling result. A signal-to-noise ratio is also presented to explain this counterintuitive phenomenon. 相似文献
15.
针对合作对策中支付函数是区间数的情形,利用区间数运算的性质,对Shapley值在经典意义下的三条公理进行拓广,并论证了该形式下的Shapley 函数的唯一形式,并将区间Shapley值方法应用到供应链协调利益分配的实例中.由于支付函数是区间数,本文最终给出的分配的结果也是一个区间数.通过证明可知,由各个联盟对应区间支付范围内的不同实数值所组成的对策是经典合作对策,并且其Shapley值一定包含在区间Shapley值中. 相似文献
16.
《数学的实践与认识》2017,(23)
随着社会发展与进步,合作共赢已经成为一种共识,但人们出于自身利益的考虑,在合作的过程中总是希望自身利益最大,这就是合作博弈.合作博弈研究的问题就是要找到一个恰当的收益分配方案,使参加合作的所有利益主体愿意合作.这里考虑两人合作共同加工一批有交货期的工件排序博弈问题.每人提供一台机器用于工件的加工,工件加工时间是开工时间的简单线性函数,以最小的最大延误作为加工成本.设计一个多项式时间动态规划算法寻找到一个合理的博弈解集,由合作双方在解集中选定最终的合作收益分配方案,即找到最终的博弈解. 相似文献
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18.
利用随机拓扑度理论研究随机非线性凝聚算子,在一定条件下得到随机算子方程A(w,x)=μx的随机解和随机算子不动点的存在性,所得结论减弱了已知文献中相应定理的条件. 相似文献
19.
关于随机算子方程的随机解 总被引:29,自引:2,他引:27
本文研究了随机算子方程(A(ω,x)=μx,(ω,x)∈Ω×D,μ1)的随机解,得到了若干新的结果,同时,我们推广了著名的Altman定理. 相似文献
20.
具有对角线化的一致质量矩阵的协调动力有限元 总被引:1,自引:0,他引:1
本文系统地研究了具有对角线化的一致质量矩阵的协调动力有限元.前文[1],[2]中,作者研究了具有对角线化的一致质量矩阵的动力有限元,并用此处理弹塑性撞击问题,但这些有限元都是不协调的.本文对空间四面体有限元和轴对称的三角环有限元求得了既有对角线化的一致质量矩阵,又有协调性质的形函数.这种有限元既可以用来处理撞击等和时间过程有关的问题,也可以处理振动计算,包括线性和非线性问题. 相似文献