重复模糊合作对策解的研究
|
摘要
对策论中,模糊对策和重复对策逐渐受到关注并成为研究热点。而在合作对策中得到广泛研究的就是在不确定环境下的对策理论研究,模糊合作对策就是其中研究方向之一,它的研究重点集中于局中人参与结盟程度模糊化条件下合作对策解的求解;支付函数模糊化条件下合作对策解的求解。这些具有模糊信息的合作可统称为模糊合作对策。对于这两个研究重点,人们提出各种各样解的概念。每种都满足一定的理性和合理性原则,论文重点研究了第一种模糊合作对策情形。
论文主要是在第一种模糊合作对策模型下加入重复合作对策理论,建立了重复模糊合作对策模型,在模糊结盟处于不同的约束条件下,给出了重复n人模糊合作对策的核心几种不同的结构,即阶段模糊对策核心的结构,重复n人模糊合作对策核心、优超核心、恰当核心、常义核心的结构,并讨论了它们之间的关系。并且对重复凸模糊合作对策这一比较重要而又特殊的对策作了研究。此外,论文进一步对重复模糊合作对策核心的特征作了研究。
论文是如下组织的:首先介绍对策论的发展史,论文产生的背景以及论文研究的实用价值。其次通过对重复合作对策优超关系的重新定义,给出了重复合作对策的弱核心、弱稳定集的概念,并对解满足的性质进行了研究。接下来介绍了模糊合作对策和重复模糊合作对策的各种解。在模糊结盟处于不同的约束条件下,给出了重复n人模糊合作对策的稳定集和核心几种不同的结构,并讨论了它们的性质及其之间的关系,研究了重复凸模糊合作对策。最后研究了重复模糊合作对策核心的特征。
In game theory, A fuzzy game and a repeated game has received a generous concern from scholars and become a research focus in academia. The most studied problem in the cooperative game is the study of game theory in uncertain circumstance. The fuzzy cooperative game is one of its research. Its research focus on players who participate in the degree of fuzzy coalition to solve; To solve cooperative game as pay function in fuzzy circumstance. Those cooperative game with fuzzy information can refer to as the fuzzy cooperative game. For the two research points, people put forward to all sorts of solution concepts .but every satisfies to rational and the principle of rationality. The paper focus on the first fuzzy cooperative game situation.
The main thesis is the fuzzy cooperative model by adding repeat cooperative game theory, set up repeat fuzzy cooperative model.It is given several differently structure of core under different condition in the fuzzy allocation n-person fuzzy cooperative game, That is, the structure of core for stage game,the structure of core and proper core and dominance core and crisp core for repeated fuzzy cooperative game .as well as discussed relation each other.And we study repeated convex fuzzy cooperative game. In addition, the paper study the core characteristics of the repeated fuzzy cooperative game .
The paper is organized as follows: First,providing histories of classical games theory, background and practical value of the paper. Second,we give the conception of core、weak core, stable set and weak stable set by redefining the notion of domination, then discuss the properties of these solutions in repeated cooperative game.The next we introduce core ,stable set and some basic theories of the fuzzy cooperative game and repeated fuzzy cooperative game. It is given several differently structure of core under different condition in the fuzzy allocation n-person fuzzy cooperative game as well as discussed relation each other.And we study the convex fuzzy cooperative game which is a type of special and important model.Finally, we take the model of reduced game,has joined repeated theory, has established repeated fuzzy reduced game model. We study their core axiomatic characteristics of the game.
论文主要是在第一种模糊合作对策模型下加入重复合作对策理论,建立了重复模糊合作对策模型,在模糊结盟处于不同的约束条件下,给出了重复n人模糊合作对策的核心几种不同的结构,即阶段模糊对策核心的结构,重复n人模糊合作对策核心、优超核心、恰当核心、常义核心的结构,并讨论了它们之间的关系。并且对重复凸模糊合作对策这一比较重要而又特殊的对策作了研究。此外,论文进一步对重复模糊合作对策核心的特征作了研究。
论文是如下组织的:首先介绍对策论的发展史,论文产生的背景以及论文研究的实用价值。其次通过对重复合作对策优超关系的重新定义,给出了重复合作对策的弱核心、弱稳定集的概念,并对解满足的性质进行了研究。接下来介绍了模糊合作对策和重复模糊合作对策的各种解。在模糊结盟处于不同的约束条件下,给出了重复n人模糊合作对策的稳定集和核心几种不同的结构,并讨论了它们的性质及其之间的关系,研究了重复凸模糊合作对策。最后研究了重复模糊合作对策核心的特征。
In game theory, A fuzzy game and a repeated game has received a generous concern from scholars and become a research focus in academia. The most studied problem in the cooperative game is the study of game theory in uncertain circumstance. The fuzzy cooperative game is one of its research. Its research focus on players who participate in the degree of fuzzy coalition to solve; To solve cooperative game as pay function in fuzzy circumstance. Those cooperative game with fuzzy information can refer to as the fuzzy cooperative game. For the two research points, people put forward to all sorts of solution concepts .but every satisfies to rational and the principle of rationality. The paper focus on the first fuzzy cooperative game situation.
The main thesis is the fuzzy cooperative model by adding repeat cooperative game theory, set up repeat fuzzy cooperative model.It is given several differently structure of core under different condition in the fuzzy allocation n-person fuzzy cooperative game, That is, the structure of core for stage game,the structure of core and proper core and dominance core and crisp core for repeated fuzzy cooperative game .as well as discussed relation each other.And we study repeated convex fuzzy cooperative game. In addition, the paper study the core characteristics of the repeated fuzzy cooperative game .
The paper is organized as follows: First,providing histories of classical games theory, background and practical value of the paper. Second,we give the conception of core、weak core, stable set and weak stable set by redefining the notion of domination, then discuss the properties of these solutions in repeated cooperative game.The next we introduce core ,stable set and some basic theories of the fuzzy cooperative game and repeated fuzzy cooperative game. It is given several differently structure of core under different condition in the fuzzy allocation n-person fuzzy cooperative game as well as discussed relation each other.And we study the convex fuzzy cooperative game which is a type of special and important model.Finally, we take the model of reduced game,has joined repeated theory, has established repeated fuzzy reduced game model. We study their core axiomatic characteristics of the game.
引文
1 V. Neumann, Morgenstern.Theory of games and economic behavior. Princeton University Press, 1944
2 J. Nash. Equilibrium Points in n-Person Game.Proc.Nat.Acad.Sci.U.S.A.,1950,36: 48-49
3 W.A. Lucas. Game with no Solution.Bull.Amer.Math.Soc,1968,74:237-239
4 G. Owen. Values of Game without Side Payments. International Journal of Game Theory,1971,1:95-109
5 L.S. Shapley. A value for N-Person Games. Ann of Math.Studies,1953,28:307-295
6 E. Kalai, D. Samet. On Weighted Shapley Values. International Journal of Game Theory, 1987,8:389-405
7 E. Kalai, D. Samet. Weighted Shapley Values. Roth AE(ed), The Shapley Vaule: Essays in honor of Lloyd S.Shapley. New York: Cambride University Press, 1988:83-99
8 R.J. Aumann, M. Maschler. The Bargaining Set for Cooperative Games. In Dresher M, Shapley LS and Tucker AW. (ed) Advances in Game Theory, Princeton University Press,1964:443-476
9 M. Davis, M. Maschler. The Kernel of A Cooperative Game. Naval Research Quarterly,1965,12:223-259
10 D. Schmeidler. The Nucleolus of A Characteristic Function Game. Slam J. Appl. Math,1969,17:1163-1170
11 S.H. Tijs. Bouds for the Core and theτ-Value. Game Theory and Mathematical Econometrical,1980,48:457-465
12 S.H. Tijs. An Axiomatization of theτ-Value. Math. Soc. Sciences,1987,13:177-181
13王先甲,陈珽.合作对策的一种新的分配方式.控制与决策,1995,5:232-237
14王先甲,陈珽.合作对策的σ值和τ值与协商解得一致性.华中理工大学学报,1995,5:41-47
15 L.A. Zadel. Fuzzy sets. Information and Control,1965,8:338-353
16 J.P. Aubin. Coeur Et Valeur Des Jeux FlousàPaiement Latéraux. CR. Acad. Sei. Paris, 1974,279A:891-894
17 R.K. Ragade. Fuzzy Games in the Analysis of Options. J. Cybern,1976,(6):213-221
18 S.A. Orlovsky. On Programming with Fuzzy Constrain Sets. Kybernets,1977,(6): 197-201
19 D. Butnariu.Value and Cores of Fuzzy Games with Infinitely Many Players. Internat. J. Game Theory,1987, (1):43-68
20 Marutyan, Eremya. An Analogue of the Shapley Function for Fuzzy Cooperative Games. Mat. Matody v Sotsial. Nauk,1987,(20):47-61
21 D. Butnariu. Fuzzy Games: A Description of the Concept. Int. J. Fuzzy Sets and Systems. 128 Shamandy. Ali. Varga. Zoltan. On An Infinite-person Dynamic Coalition Game. Ann. Univ. Sci. Budapest. Sect. Comput,1987,(7):149-154
22 L. Campos. Fuzzy Linear Programming Models to Solve Fuzzy Matrix Games. Fuzzy Sets and Systems,1989,(3):275-289
23赵景柱.和—合成模糊对策和模糊稳定集.中国科学院研究生院学报,1994,11(1):92-96
24 M. Mare?. Fuzzy Coalition Structure. Fuzzy sets and Systems,2000,114:23-33
25 W.K. Kim, K.H. Lee. Generalized Fuzzy Games and Fuzzy Equilibria. Fuzzy Sets and Systems,2001,(122):293-301
26 M. Tsurumi, T. Tanino. A Shapley Function on A Class of Cooperative Games. Eur. J. Ope. Res,2001,129:596-618
27 R. Branzei, D. Dimitrov, S. Tijs. Convex Fuzzy Games and Participation Monotonic Allocation Schemes. Fuzzy Sets and Systems,2003,139:267-281
28 R. Branzei, D. Dimitrov, S.Tijs. Hypercubes and Compromise Values for Cooperative Fuzzy Games. European Journal of Operational Research, 2004,(155): 733-740
29 S. Tijs, R. Branzei, S. Ishihara, S. Muto. On Cores and Stable Sets for Fuzzy Games. Fuzzy Sets and Systems,2004,146:285-296
30 R. Branzei, D. Dimitrov, S.Tijs. Egalitarianism in Convex Fuzzy Games.MathmaticalSocial Sciences, 2004,47:313-325
31 S. Tijs. R. Branzei, S. Muto, S. Ishihara, E. Fukuda. Fuzzy Clan Games and Bi-monotonic Allocation Rules. Fuzzy Sets and Systems,2004,(146):271-284
32张凤荣,张盛开,谢里阳.效用不可转移的模糊结盟对策.系统工程,2004,(10): 13-15
33谢政.对策论.武汉:国防科技大学出版社,2004,183-241
34高红伟.结盟对策中弱稳定集的引入与探讨.青岛大学学报,1998,11(4):1-4
35 R.J. Aumann, M. Maschler. Repeated Games in Incomplete Information. A survey of Recent Results Mathematic. Chapter III, 1967
36 R.J. Aumann, M. Maschler. Repeated Games of Incomplete Information: An Approach to the Non-zero-sum Case. Mathematic. Chapter IV, 1968
37 E. Kohlberg. Optimal Strategies in Repeated Game of Incomplete Information. International Journal of Game Theory, 1975, 4:7-24
38 E. Kalai, W. Stanford. Finite Rationality and Interpersonal Complexity in Repeated Games. Econometrica, 1988(2), 56
39 E. Kalai, Bounded Rationality and Strategic Complexity in Repeated Games. Edited by T .Ichiishi, A .Neynar, Y .Tauman. Academic Press Inc,1990:131-157
40 I. Nabil, A.Najjar, R.Smorodininsky. Large Nonanonymous Repeated Games. Games and Economic Behabior,2001,37:26-39
41 Y. Breitmoser. Infinitely Reapeated Games of Reciprocal Players. Economics Letters,2005,89:323-327
42 I. Cho, A. Matsui. Learning Aspiration in Repeated Games.Journal of Economic Theory ,2005,124:171-201
43 I. Engle-Warnick, L. Robert.slonim..Learning to Trust in Indefinitely Repeated Games .Games and Economic Behabior,2006,54:95-114
44 J. Oviedo. The Core of a Repeated n-person Cooperative Game. European Journalof Operational Research, 2000, 127:519-524
45 Y.A. Hwang,The characterizations of the consistent egalitarian solution and of the core on NTU games.ZOR-Math.Methods Oper.Res, 2006,64:557-568
46高作峰,王艳,张向东.凸合成模糊对策的模糊稳定集.运筹与管理,2004,13(1):59-62
47刘广智,邹开其,王丽琦.一般化合成模糊对策解的结构.系统工程理论与实践,2005,(4):90-102
48刘广智,邹开其.一般化合成模糊对策的势指标.模糊系统与数学,2005,19(2):16-121
49张凤荣,张盛开.关于多个模糊集对策的合成对策.辽宁工程技术大学学报,2006,25(4):632-634
50吴伟,赵景柱.M和—合成对策的Branzhaf-Coleman势指标.大连理工大学学报,1989,29(1):121-124
51王艳,高作峰,张盛开.有限制结盟的NTU对策解.高校应用数学学报A辑,2006,21(3):271-277
52乔晗,高红伟,程凌.用弱优超的概念改造NTU对策的核心.青岛大学学报(自然科学版),2004,17(专刊):63-65
53罗党,吴顺祥.带有灰色约束的二人有限零和博弈研究.厦门大学学报(自然科学版),2006,45(1):29-31
54 L.S. Shapley, Shubik. A Method for Evaluating the Distribution of Power in Committee System. Amer Politi.Sci.Review,1954,48:787-792
55 L.S. Shapley. Utility Comparision and the Theory of Games. La decision 2, 1969:251-163
56 D.B. Gillies. Solution to General Non-Zero Games.Ann.Math.Stud,1959,40:47-85
57 L.J. Billera. Some Theorems on the Core of a n-Person Games without Side Payments. SLAM J.Appl.Math,1970,18:567-579
58 J.P. Aubin. Cooperative Fuzzy Game. Math.O.R,1981,(1):1-13
59 Manuel A. Pulido*, Joaquin Sanchez-Soriano. Characterization of the core in games with restricted cooperation. European Journal of Operational Reseach,2006,175:860 -869
60 J.M. Izquierdo, Carles Rafels, Average Monotonic Cooperative Games. Games and Economic Behavior,2001,36:174-192
61 Y.A. Hwang. Fuzzy games :A characterization of the core. Fuzzy Sets and Systems, 2007,3:1-14
62 R. Somal. New Algorithms for Solving Simple Stochastic Games. Electronic Notes in Theoretical Computer Science,2005,19:51-65
63 N. Vieille. Small Perturbations and Stochastic Games. Math,2002,119B:127-144
64 J. E. Warnick, L. Robert. Slonim. Learning to Trust in Indefinitely Repeated Games. Games and Economic Behavior,2006,54:95-114
65 I. Cho, A. Matsui. Learning Aspiration in Repeated Games. Journal of Economic Theory,2005,124:171-201
66杜河建.一个博弈的模糊延拓方法.模糊系统与数学,2006,20(4):91-96
67张青,胡子祥,黄天民.混合模糊多目标多人非合作对策及其解.江南大学学报(自然科学版),2005,4(1):94-96
68高作峰,徐东方,鄂成国,王彩虹.重复模糊合作对策的核心和稳定集.运筹与管理,2006,15(4):68-72
69徐东方,高作峰,鄂成国,王彩虹.大老板对策的广义核心和妥协值.燕山大学学报,2006,30(3):243-246
70姜殿玉.连续对策上的计策理论.系统工程,2003,21(1):1-7
71 B. Arma. Shapley Value for Constant-sum Games. Int J Game Theory,2003,(32):223 -227
72 H. W. Kuhn, A. W. Tucker. Annals of Mathematics Studies. University Press Princeton,2003,28:307-312
73 R.P. Gilles, G. Owen, Brink, R.V. Den. Games with Permission Structures: the Conjunctive Approach. International Journal of Game Theory,1992,20:277-293
74刘德铭,黄振高.对策论及其应用.武汉:国防科技大学出版社,1994
75鄂成国.重复随即合作对策的解.中国优秀硕士论文全文数据库,2006
76高作峰,王友,王国成.对策理论与经济管理决策.北京:中国林业出版社,2006
77张盛开,张亚东.现代对策(博弈)论与工程决策方法.大连:东北财经大学出版社,2005
78王建华.对策论.北京:清华大学出版社,1986
79 [加]杨荣基,[俄]彼得罗相,[香港]李颂志等,动态合作-尖端博弈论.中国市场出版社,2007
2 J. Nash. Equilibrium Points in n-Person Game.Proc.Nat.Acad.Sci.U.S.A.,1950,36: 48-49
3 W.A. Lucas. Game with no Solution.Bull.Amer.Math.Soc,1968,74:237-239
4 G. Owen. Values of Game without Side Payments. International Journal of Game Theory,1971,1:95-109
5 L.S. Shapley. A value for N-Person Games. Ann of Math.Studies,1953,28:307-295
6 E. Kalai, D. Samet. On Weighted Shapley Values. International Journal of Game Theory, 1987,8:389-405
7 E. Kalai, D. Samet. Weighted Shapley Values. Roth AE(ed), The Shapley Vaule: Essays in honor of Lloyd S.Shapley. New York: Cambride University Press, 1988:83-99
8 R.J. Aumann, M. Maschler. The Bargaining Set for Cooperative Games. In Dresher M, Shapley LS and Tucker AW. (ed) Advances in Game Theory, Princeton University Press,1964:443-476
9 M. Davis, M. Maschler. The Kernel of A Cooperative Game. Naval Research Quarterly,1965,12:223-259
10 D. Schmeidler. The Nucleolus of A Characteristic Function Game. Slam J. Appl. Math,1969,17:1163-1170
11 S.H. Tijs. Bouds for the Core and theτ-Value. Game Theory and Mathematical Econometrical,1980,48:457-465
12 S.H. Tijs. An Axiomatization of theτ-Value. Math. Soc. Sciences,1987,13:177-181
13王先甲,陈珽.合作对策的一种新的分配方式.控制与决策,1995,5:232-237
14王先甲,陈珽.合作对策的σ值和τ值与协商解得一致性.华中理工大学学报,1995,5:41-47
15 L.A. Zadel. Fuzzy sets. Information and Control,1965,8:338-353
16 J.P. Aubin. Coeur Et Valeur Des Jeux FlousàPaiement Latéraux. CR. Acad. Sei. Paris, 1974,279A:891-894
17 R.K. Ragade. Fuzzy Games in the Analysis of Options. J. Cybern,1976,(6):213-221
18 S.A. Orlovsky. On Programming with Fuzzy Constrain Sets. Kybernets,1977,(6): 197-201
19 D. Butnariu.Value and Cores of Fuzzy Games with Infinitely Many Players. Internat. J. Game Theory,1987, (1):43-68
20 Marutyan, Eremya. An Analogue of the Shapley Function for Fuzzy Cooperative Games. Mat. Matody v Sotsial. Nauk,1987,(20):47-61
21 D. Butnariu. Fuzzy Games: A Description of the Concept. Int. J. Fuzzy Sets and Systems. 128 Shamandy. Ali. Varga. Zoltan. On An Infinite-person Dynamic Coalition Game. Ann. Univ. Sci. Budapest. Sect. Comput,1987,(7):149-154
22 L. Campos. Fuzzy Linear Programming Models to Solve Fuzzy Matrix Games. Fuzzy Sets and Systems,1989,(3):275-289
23赵景柱.和—合成模糊对策和模糊稳定集.中国科学院研究生院学报,1994,11(1):92-96
24 M. Mare?. Fuzzy Coalition Structure. Fuzzy sets and Systems,2000,114:23-33
25 W.K. Kim, K.H. Lee. Generalized Fuzzy Games and Fuzzy Equilibria. Fuzzy Sets and Systems,2001,(122):293-301
26 M. Tsurumi, T. Tanino. A Shapley Function on A Class of Cooperative Games. Eur. J. Ope. Res,2001,129:596-618
27 R. Branzei, D. Dimitrov, S. Tijs. Convex Fuzzy Games and Participation Monotonic Allocation Schemes. Fuzzy Sets and Systems,2003,139:267-281
28 R. Branzei, D. Dimitrov, S.Tijs. Hypercubes and Compromise Values for Cooperative Fuzzy Games. European Journal of Operational Research, 2004,(155): 733-740
29 S. Tijs, R. Branzei, S. Ishihara, S. Muto. On Cores and Stable Sets for Fuzzy Games. Fuzzy Sets and Systems,2004,146:285-296
30 R. Branzei, D. Dimitrov, S.Tijs. Egalitarianism in Convex Fuzzy Games.MathmaticalSocial Sciences, 2004,47:313-325
31 S. Tijs. R. Branzei, S. Muto, S. Ishihara, E. Fukuda. Fuzzy Clan Games and Bi-monotonic Allocation Rules. Fuzzy Sets and Systems,2004,(146):271-284
32张凤荣,张盛开,谢里阳.效用不可转移的模糊结盟对策.系统工程,2004,(10): 13-15
33谢政.对策论.武汉:国防科技大学出版社,2004,183-241
34高红伟.结盟对策中弱稳定集的引入与探讨.青岛大学学报,1998,11(4):1-4
35 R.J. Aumann, M. Maschler. Repeated Games in Incomplete Information. A survey of Recent Results Mathematic. Chapter III, 1967
36 R.J. Aumann, M. Maschler. Repeated Games of Incomplete Information: An Approach to the Non-zero-sum Case. Mathematic. Chapter IV, 1968
37 E. Kohlberg. Optimal Strategies in Repeated Game of Incomplete Information. International Journal of Game Theory, 1975, 4:7-24
38 E. Kalai, W. Stanford. Finite Rationality and Interpersonal Complexity in Repeated Games. Econometrica, 1988(2), 56
39 E. Kalai, Bounded Rationality and Strategic Complexity in Repeated Games. Edited by T .Ichiishi, A .Neynar, Y .Tauman. Academic Press Inc,1990:131-157
40 I. Nabil, A.Najjar, R.Smorodininsky. Large Nonanonymous Repeated Games. Games and Economic Behabior,2001,37:26-39
41 Y. Breitmoser. Infinitely Reapeated Games of Reciprocal Players. Economics Letters,2005,89:323-327
42 I. Cho, A. Matsui. Learning Aspiration in Repeated Games.Journal of Economic Theory ,2005,124:171-201
43 I. Engle-Warnick, L. Robert.slonim..Learning to Trust in Indefinitely Repeated Games .Games and Economic Behabior,2006,54:95-114
44 J. Oviedo. The Core of a Repeated n-person Cooperative Game. European Journalof Operational Research, 2000, 127:519-524
45 Y.A. Hwang,The characterizations of the consistent egalitarian solution and of the core on NTU games.ZOR-Math.Methods Oper.Res, 2006,64:557-568
46高作峰,王艳,张向东.凸合成模糊对策的模糊稳定集.运筹与管理,2004,13(1):59-62
47刘广智,邹开其,王丽琦.一般化合成模糊对策解的结构.系统工程理论与实践,2005,(4):90-102
48刘广智,邹开其.一般化合成模糊对策的势指标.模糊系统与数学,2005,19(2):16-121
49张凤荣,张盛开.关于多个模糊集对策的合成对策.辽宁工程技术大学学报,2006,25(4):632-634
50吴伟,赵景柱.M和—合成对策的Branzhaf-Coleman势指标.大连理工大学学报,1989,29(1):121-124
51王艳,高作峰,张盛开.有限制结盟的NTU对策解.高校应用数学学报A辑,2006,21(3):271-277
52乔晗,高红伟,程凌.用弱优超的概念改造NTU对策的核心.青岛大学学报(自然科学版),2004,17(专刊):63-65
53罗党,吴顺祥.带有灰色约束的二人有限零和博弈研究.厦门大学学报(自然科学版),2006,45(1):29-31
54 L.S. Shapley, Shubik. A Method for Evaluating the Distribution of Power in Committee System. Amer Politi.Sci.Review,1954,48:787-792
55 L.S. Shapley. Utility Comparision and the Theory of Games. La decision 2, 1969:251-163
56 D.B. Gillies. Solution to General Non-Zero Games.Ann.Math.Stud,1959,40:47-85
57 L.J. Billera. Some Theorems on the Core of a n-Person Games without Side Payments. SLAM J.Appl.Math,1970,18:567-579
58 J.P. Aubin. Cooperative Fuzzy Game. Math.O.R,1981,(1):1-13
59 Manuel A. Pulido*, Joaquin Sanchez-Soriano. Characterization of the core in games with restricted cooperation. European Journal of Operational Reseach,2006,175:860 -869
60 J.M. Izquierdo, Carles Rafels, Average Monotonic Cooperative Games. Games and Economic Behavior,2001,36:174-192
61 Y.A. Hwang. Fuzzy games :A characterization of the core. Fuzzy Sets and Systems, 2007,3:1-14
62 R. Somal. New Algorithms for Solving Simple Stochastic Games. Electronic Notes in Theoretical Computer Science,2005,19:51-65
63 N. Vieille. Small Perturbations and Stochastic Games. Math,2002,119B:127-144
64 J. E. Warnick, L. Robert. Slonim. Learning to Trust in Indefinitely Repeated Games. Games and Economic Behavior,2006,54:95-114
65 I. Cho, A. Matsui. Learning Aspiration in Repeated Games. Journal of Economic Theory,2005,124:171-201
66杜河建.一个博弈的模糊延拓方法.模糊系统与数学,2006,20(4):91-96
67张青,胡子祥,黄天民.混合模糊多目标多人非合作对策及其解.江南大学学报(自然科学版),2005,4(1):94-96
68高作峰,徐东方,鄂成国,王彩虹.重复模糊合作对策的核心和稳定集.运筹与管理,2006,15(4):68-72
69徐东方,高作峰,鄂成国,王彩虹.大老板对策的广义核心和妥协值.燕山大学学报,2006,30(3):243-246
70姜殿玉.连续对策上的计策理论.系统工程,2003,21(1):1-7
71 B. Arma. Shapley Value for Constant-sum Games. Int J Game Theory,2003,(32):223 -227
72 H. W. Kuhn, A. W. Tucker. Annals of Mathematics Studies. University Press Princeton,2003,28:307-312
73 R.P. Gilles, G. Owen, Brink, R.V. Den. Games with Permission Structures: the Conjunctive Approach. International Journal of Game Theory,1992,20:277-293
74刘德铭,黄振高.对策论及其应用.武汉:国防科技大学出版社,1994
75鄂成国.重复随即合作对策的解.中国优秀硕士论文全文数据库,2006
76高作峰,王友,王国成.对策理论与经济管理决策.北京:中国林业出版社,2006
77张盛开,张亚东.现代对策(博弈)论与工程决策方法.大连:东北财经大学出版社,2005
78王建华.对策论.北京:清华大学出版社,1986
79 [加]杨荣基,[俄]彼得罗相,[香港]李颂志等,动态合作-尖端博弈论.中国市场出版社,2007