---------------------------------------------------------------------------------------------

, : 60774097

1 2 1 2

1 , ,110004

E-mail:xuxinhe@ise.neu.edu.cn

2 , ,110004

E-mail: jixiangruyiwy@126.com

——“ - - ”

Analysis on the Achievement Milestones and Limitations of Game Theory

XU Xinhe1, WANG Yan2, LIU Jihong1, ZHANG Xuefeng2

1 Computer Game Group, Institute of Information Science and Engineering, Northeastern University,Shenyang 110004

E-mail: xuxinhe@ise.neu.edu.cn

2 Institute of System Science, Northeastern University; Shenyang 110004, China E-mail: jixiangruyiwy@126.com

Abstract: The game issues are more complicated and difficult to be solved than the control and decision-making problems, therefore they

are more challenging. Game Theory facing to the modeling and solution of various game issues has undergone over half a century of fast

development, and has obtained a series of achievement which can been regarded as milestones. So it has played a great improving role in the

development of economics and relevant fields. After introducing the main achievement of Game Theory, the essence and the basic model of

Game Theory are summarized, i.e. “Rationality –Prediction- Equilibrium”. But when facing the complicated dynamic game systems, for

example, chess game, it is hard to solve the move problem by the current Game Theory. It seems that some limitations of Game Theory are

showed. Therefore, the Game Theory and Computer Game should be combined so that we can overcome some limitations, improve the

extension of the theory, and create a new situation for the applications of Game Theory. Keywords: Game Theory; Rationality; Consistent Prediction; Nash Equilibrium; Computer Games; Event Game

1214

978-1-4244-1734-6/08/$25.00 c© 2008 IEEE

1. (Introduction)

2070

23

4

2 (Review of Achievement Milestones of Game Theory)

1500

Waldgrave 1713Cournot A

[2] Bertrand

Edgeworth

E.Zermelo 1913[3] Backward induction

procedure E.Borel 1921 [4]

John vonNeuman 1928

[5]

John von NeumanOskar Morgenstern 1944

[6]

John Nash 1950[7]

CournotA Bertrand

Albert W.TuckerPrisoner’s Dilemma

(Reinhard Selten)1965 Subgame Perfect

2008 Chinese Control and Decision Conference (CCDC 2008) 1215

Nash Equilibrium [8]

John Harsanyi 1967-1968

[9]

Bayesian Nash Equilibrium

Sequential Equlibrium

Kreps and Wilson 1982 [10]

1975Trembling – hand Perfect Equilibrium

[11]

Signaling games

pence 1973

2001[12]

(Differential games)20

Issacs[13]

1971 Friedman

20 50(Thomas Schelling)

The Strategy of Conflict [14]

Robert Aumann

1959 Strong Equilibrium [15]

Non transferable utility1966

Michael Maschler

Interactive epistemology 1976Agreeing to disagree [16]

Lewis 1969

1216 2008 Chinese Control and Decision Conference (CCDC 2008)

2005

[1]

3.(“Rationality –Prediction–Equilibrium”--the Essence of Game Theory)

[17]

[17]

[8]

[17]

1 Bayes

1

Equilibrium outcome

4. (Analysis on Limitations of Game Theory)

2008 Chinese Control and Decision Conference (CCDC 2008) 1217

E Zermelo)

[18]

[19]

5. Discussion on the Way to Overcome the Limitations

[20]

1218 2008 Chinese Control and Decision Conference (CCDC 2008)

6. Conclusion

[1] [M] 2005.

[2] Counot,A.,recherches sur les Principes Mathematiques de la

Theorie des Richesses 1838. English edition(ed. N. Bacon):

Researches into the Mathematical Principles of the Theory of

Wealth[M] Macmillan,1897.

[3] Zermelo, E.,Uber eine Anwendung der Mengenlehre auf die

Theorie des Schachspiels[M], In Proceedings of the Fifth

International Congress on Mathematics,1913.

[4] Borel, E.,The Theory of Play and Integral Equations with Ske

Symmetric Kernels[J], Econometrica ,Vol.21,pp.97-100, 1953.

[5] Von Neumann,J.,Zur Theorie der Gesellschaftsspiele[J],Math.

Annalen,Vol,100,pp.295-320, 1928.

[6] Von Neumann, J.and Mogenstern,O.,The Theory of Games and

Economic Behavior[J].Princeton University Press, Princeton

1944.

[7] Nash, J.,Equilibrium points in N-person games,,Proceedings of

the National Academy of Sciences[J],Vol.36,pp.48-49, 1950.

[8] [M]

2002.

[9] Harsanyi, J., Games with incomplete information played by

Bayesian players[J], Management Science,Vol. 14, pp.159-182,

320-334,486-502, 1967.

[10] Kreps, D.,and R. Wilson., Sequential Equilibria[J],

Econometrica, Vol. 50,pp.863-894, 1982.

[11] Selten, R., Re-examination of the perfectness concept for

equilibrium points in extensive games[J], International Journal of

Game Theory,Vol. 4,pp.25-55, 1975.

[12] Spence, A.M., Job Marketing Signaling,Journal of Economic

Theory[J],Vol.8,pp.296-332, 1973.

[13] Issacs R, Differential Games[M]. New York: John Wiley &

Sons,1965.

[M]

2006.

[15] Aumann, R., Acceptable points in general cooperative

n-person[M],In contributions to the Theory of Games IV.Priceton

University Press,1959.

[16] Aumann, R., Agreeing to disagree[J],Annals of Statistics, Vol.4,

pp.1236-1239, 1976.

[17] , 3 [M]. ,

,2002.

[18] , [M]. ,

,2004.

[19] , [M]. , 1999,7.

[20] Breakthrough of the year, Science[J], Vol. 318 pp.1842-1849

2007.

[21] . [J].

Vol.22, No.7(2007.7): 787-790

[22] . [C]. 2007

: 913-916 2007.7.5 8

2008 Chinese Control and Decision Conference (CCDC 2008) 1219