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N-person credibilistic strategic game |
Rui LIANG1, Yueshan YU2, Jinwu GAO3( ), Zhi-Qiang LIU4 |
1. School of Economics and Finance, Xi’an Jiaotong University, Shaanxi 710049, China; 2. Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China; 3. School of Information, Renmin University of China, Beijing 100872, China; 4. School of Creative Media, City University of HongKong, Hong Kong, China |
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Abstract This paper enlarges the scope of fuzzy-payoff game to n-person form from the previous two-person form. Based on credibility theory, three credibilistic approaches are introduced to model the behaviors of players in different decision situations. Accordingly, three new definitions of Nash equilibrium are proposed for n-person credibilistic strategic game. Moreover, existence theorems are proved for further research into credibilistic equilibrium strategies. Finally, two numerical examples are given to illustrate the significance of credibilistic equilibria in practical strategic games.
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Keywords
fuzzy variable
credibility measure
strategic game
credibilistic equilibrium
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Corresponding Author(s):
GAO Jinwu,Email:jgao@ruc.edu.cn
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Issue Date: 05 June 2010
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1 |
Nash J F. Equilibrium points in n-person games. Proceedings of the National Academy of Sciences of the United States of America , 1950, 36(1): 48-49 doi: 10.1073/pnas.36.1.48
|
2 |
Nash J. Non-cooperative games. Annals of Mathematics , 1951, 54(2): 286-295 doi: 10.2307/1969529
|
3 |
Harsanyi J C. Games with incomplete information. American Economic Review , 1995, 85: 291-303
|
4 |
Blau R A. Random-payoff two-person zero-sum games. Operations Research , 1974, 22(6): 1243-1251 doi: 10.1287/opre.22.6.1243
|
5 |
Cassidy R G, Field C A, Kirby M J L. Solution of a satisficing model for random payoff games. Management Science , 1972, 19(3): 266-271 doi: 10.1287/mnsc.19.3.266
|
6 |
Zadeh L A. Fuzzy sets. Information and Control , 1965, 8(3): 338-353 doi: 10.1016/S0019-9958(65)90241-X
|
7 |
Maeda T. Characterization of the equilibrium strategy of the bimatrix game with fuzzy payoff. Journal of Mathematical Analysis and Applications , 2000, 251(2): 885-896 doi: 10.1006/jmaa.2000.7142
|
8 |
Campos L, Gonzalez A, Vila M A. On the use of the ranking function approach to solve fuzzy matrix games in a direct way. Fuzzy Sets and Systems , 1992, 49(2): 193-203 doi: 10.1016/0165-0114(92)90324-W
|
9 |
Nishizaki I, Sakawa M. Equilibrium solutions for multiobjective bimatrix games with fuzzy payoffs and fuzzy goals. Fuzzy Sets and Systems , 2000, 111(1): 99-116 doi: 10.1016/S0165-0114(98)00455-2
|
10 |
Liu B. Uncertainty Theory: An Introduction to Its Axiomatic Foundations. Springer-Verlag, Berlin, 2004
|
11 |
Liu B. Uncertainty Theory. Springer-Verlag, Berlin, 2nd edition, 2007.
|
12 |
Liu B. A survey of credibility theory. Fuzzy Optimization and Decision Making , 2006, 5(4): 387-408 doi: 10.1007/s10700-006-0016-x
|
13 |
Gao J. Credibilistic game with fuzzy information. Journal of Uncertain Systems , 2007, 1(1): 74-80
|
14 |
Gao J, Liu Z Q, Shen P. On characterization of credibilistic equilibria of fuzzy-payoff two-player zero-sum game. Soft Computing , 2009, 13(2): 127-132 doi: 10.1007/s00500-008-0310-3
|
15 |
Shen P, Gao J. Colitional game with fuzzy payoffs and the credibilistic core. Soft Computing , 2010, (to be published) doi: 10.1007/s00500-010-0562-6
|
16 |
Yu Y, Gao J. Credibilistic extensive game with fuzzy payoffs. Technical Report of Renmin University of China , 2008
|
17 |
Gao J, Liu B. Fuzzy multilevel programming with a hybrid intelligent algorithm. Computers & Mathematics with Applications (Oxford, England) , 2005, 49(9-10): 1539-1548 doi: 10.1016/j.camwa.2004.07.027
|
18 |
Osborne M J, Rubinstein A. A Course In Game Theory. The MIT Press, Cambridge, Massachusetts and London, England, 1994
|
19 |
Zadeh L A. Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems , 1978, 1(1): 3-28 doi: 10.1016/0165-0114(78)90029-5
|
20 |
Dubois D, Prade H. Possibility Theory. Plenum, New York, 1988
|
21 |
Liu B, Liu Y. Expected value of fuzzy variable and fuzzy expected value models. IEEE Transactions on Fuzzy Systems , 2002, 10(4): 445-450 doi: 10.1109/TFUZZ.2002.800692
|
22 |
Liu Y, Gao J. The independence of fuzzy variables with applications to fuzzy random optimization. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems , 2007, 15(SUPPL. 2): 1-20 doi: 10.1142/S021848850700456X
|
23 |
Liu Y, Liu B. Expected value operator of random fuzzy variable and random fuzzy expected value models. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems , 2003, 11(2): 195-215 doi: 10.1142/S0218488503002016
|
24 |
Osborne M J. An Introduction to Game Theory. Oxford University Press, 2004
|
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