Aplikasi Geometri pada Permainan Dinamis Non-Kooperatif Skalar Waktu tak Berhingga

Nilwan Andiraja


In this research was discuss about to find equilibrium Nash in non-cooperative dynamic game two-player with scalar case for infinite time, by application the analytic geometry. Discuss was started from made of equation model for non-cooperative dynamic game two-player with scalar case for infinite time based on equation of non-cooperative dynamic game for infinite time. Then made of two the algebraic Riccati equation and control vector for each player. The control vector is used for made of stability condition of game. Then is used the curse of analytic geometry for analyse equilibrium Nash for dynamic game. Base on analyse, there are two algebraic Riccati equation which it is special case of the algebraic of second degree which it is hyperbolic equation. Then, based on of stability condition of game then equilibrium Nash can get from intersection point of two hyperbolic in adequate area for stability condition of game.
Keywords: Dynamic, Game ,Geometry, Riccati, Scalar

Full Text:



. Basar T. Dynamic noncooperative game theory. Philadelphia: SIAM. 1999.

Bellman R. Introduction to Matrix Analysis. Philadelphia: SIAM. 1997

Engwerda J. Feedback Nash equilibria in the scalar infinite horizon LQ-game. Automatica. 2000; 36 :


Engwerda J. LQ Dynamic Optimization and Differential Games. Chichester: John Wiley & Sons. 2005.

Lewis FL. Applied Optimal Control and Estimation. New Jersey: Prentice-Hall, Inc. 1992.

Olsder GJ. Mathematical System Theory. Delft: University of Technology. 1994.

Perko L. Differential Equations and Dynamical System. New York: Springer-Verlag. 1991.

Weeren AJTM, Schumacher JM, Engwerda J. Asymptotic analysis of linear feedback Nash equilibria

in nonzero-sum linear-quadratic differential games. Journal of Optimization Theory and

Applications.1999: 101: p693–723.


  • There are currently no refbacks.


Kampus Raja Ali Haji
Gedung Fakultas Sains & Teknologi UIN Suska Riau
Jl.H.R.Soebrantas No.155 KM 18 Simpang Baru Panam, Pekanbaru 28293
Email: sntiki@uin-suska.ac.id