PERMAINAN DINAMIS LINGKAR TERBUKA LINEAR KUADRATIS SISTEM DESKRIPTOR DAN APLIKASINYA PADA INTERAKSI FISKAL MONETER
Abstract. In this paper we will study linear quadratic continuous non-zero-sum two player dynamic games for descriptor system. In application for economic problem we need to include discounting factor in the cost function. We assume that the structure of the game is open loop. To find Nash equilibri...
| Main Authors: | , , |
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| Format: | Book Section |
| Language: | English |
| Published: |
2009
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| Subjects: | |
| Online Access: | https://repository.ugm.ac.id/101245/1/32.pdf |
| Summary: | Abstract. In this paper we will study linear quadratic continuous non-zero-sum two player dynamic games for descriptor system. In application for economic problem we need to include discounting factor in the cost function. We assume that the structure of the game is open loop. To find Nash equilibrium solution of the game we will relate to solution of Riccati equation. Non-recursive formulae for solution of algebraic Riccati equation for game with infinite horizon case will be derived.
Fiscal monetary interaction among nations naturally will be a linear quadratic dynamic game model. In this paper the model will be consider in the framework of linear quadratic dynamic game descriptor system. In the objective function as usually happened in economic problem, there is a discounting factor. For analyzing further the model will be brought to a standard linear quadratic dynamic game. Then the numerical formulae for the solution of linear quadratic dynamic game descriptor system is applied for fiscal monetary interaction among nation problem. Stability of the controlled system will be analyze by consider the eigen values of the closed loop system.
Abstrak. Dalam makalah ini akan dikaji permainan dinamis linear kuadratis tak berjumlah nol untuk sistem deskriptor. Pada aplikasi untuk masalah ekonomi diperlukan memasukkan faktor discounting pada fungsi objektif. Diasumsikan bahwa struktur permainan adalah lingkar terbuka. Mencari penyelesaian optimal Nash permainan berkaitan dengan mencari penyelesaian persamaan Riccati. Rumus non-rekursif penyelesaian persamaan aljabar Riccati untuk permainan dengan horizon tak berhingga akan diturunkan.
Model interaksi fiskal moneter antar negara secara natural merupakan model permainan dinamis linear kuadratis. Pada makalah ini model tersebut akan ditinjau sebagai permainan dinamis linear kuadratis sistem deskriptor. Pada fungsi objektif sebagaimana biasanya pada model masalah ekonomi, muncul faktor discounting. Untuk menganalisa lebih lanjut model akan dibawa dahulu ke dalam model standard permainan dinamis linear kuadratis. Selanjutnya rumus non-rekursif penyelesaian permainan dinamis linear kuadratis sistem deskriptor diaplikasikan pada masalah interaksi fiskal moneter antar negara. Kestabilan hasil kendali akan diselidiki dengan mencari nilai eigen matriks lingkar tertutupnya. |
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