Uogólnione zadania sterowania optymalnego - gra dynamiczna według Nasha

• Autorzy: Krystyna Strzała

Warianty tytułu

Generalised Optimal Control Models - the Dynamic Nash Game

• Języki publikacji: PL

Abstrakty

EN

The purpose of the paper is to present methods that can be effectively used for modeling economic decision making processes with conflicting objectives of various groups of decision makers. The analyzed system is described on the basis of an econometric model. The problem is modeled within the framework of a game theoretical approach. Basic types of organizational structure are discussed, and special emphasis is put on the Nash game. Two types of information structures are distinguished and discussed in the context of a policy model with a discrete time econometric model as part of it. The paper presents algorithms used in an open-loop as well as a closed-loop information structure. The method employed for solving the problem is dynamic programming, which in the open-loop Nash game could be applied either in a global or in stage-wise mode. There are five different algorithms presented, and special emphasis is put on the generalization of Haas's algorithm, which makes it possible to apply it to the nonlinear model. (original abstract)

Słowa kluczowe

PL

Teoria gier; Teoria optymalizacji; Teoria kontroli

EN

Game theory; Optimization theory; Control theory

• Czasopismo: Przegląd Statystyczny
• Rocznik: 1996
• Tom: 43
• Numer: z. 1-2
• Strony: 131-148

Twórcy

autor

Krystyna Strzała

Bibliografia

• [1] Basar T., A Tutorial on Dynamic and Differential Games, w: T. Basar (wyd.) Dynamic Games and Applications in Economics, Springer Verlag, Berlin 1986.
• [2] Basar T., Olsder G.J., Dynamic Noncooperative Game Theory, Academic Press, London/New York 1982.
• [3] Bellman R.E., Dynamic Programming, Princeton, Nowy York 1957.
• [4] Blackburn K., Macroeconomic Policy Evaluation and Optimal Control Theory: A Critical Review of Some Recent Developments, Journal of Economic Surveys 1, 1987, s. 111-148.
• [5] Buiter W.H., The Superiority of Contingent Rules over Fixed Rules in Models with Rational Expectations, Economic Journal 91, 1981, s. 647-670.
• [6] Canon M.D., Cullum CD., Polak E., Sterowanie optymalne i programowanie matematyczne, WNT, Warszawa 1975.
• [7] Case J.H., Toward a Theory of Many Player Differential Games, SIAM Journal on Control 7, 2, 1969.
• [8] Chen C.I., Cruz J.B., Stackelberg Solution for Two-Person Games with Biased Information Patterns, IEEE Trans. Autom. Control AC-17, 6, 1972.
• [9] Chow G.C., Econometric Analysis by Control Methods, J. Wiley and Sons, Inc., New York 1981.
• [10] Chow G.C., Analysis and Control of Dynamic Economic Models, J. Wiley and Sons, Inc., New York 1975.
• [11] Cichocki K., Tołwiński B., Teoria sterowania w modelowaniu ekonomicznym. Perspektywy i trudności, w: A. Straszak (red.), Problemy modelowania i sterowania w systemach społeczno-gospodarczego rozwoju, PWN, Warszawa 1981.
• [12] Currie D. and Levine P., Macroeconomic Policy Design in an Interdependent World, in W.H. Buiter and R.C. Marston International Economic Policy Coordination, Cambridge 1984.
• [13] De Zeeuw A.J., Difference Games and Linked Econometric Policy Models, Ph.D. Thesis, Tilburg University 1984.
• [14] Fischer S., Dynamic Inconsistency, Cooperation and the Benevolent Dissembling Government, Journal of Economic Dynamics and Control 2, 1980, s. 93-107.
• [15] Haas H., Optimale Steuerung unter Bertcksichtigung mehrerer Entscheidungstraeger: nichtkooperative und kooperative Strategien in linear-quadratischen Planungsproblem, w: J. Frohn (wyd.) Methodik und Anwendung oekonometrischer Entscheidungsmodelle, Vandenhoeck & Ruprecht 1980.
• [16] Haas H., A Generalisation of Chow's Algorithm from one to m Noncooperative Controllers, Diskussionsarbeit no. 66, Universitaet Bielefeld 1979.
• [17] Harsanyi J., Rational Behaviour and Bargaining Equilibrium in Games and Social Situations, Cambridge University Press, Cambridge 1977.
• [18] Hughes Hallet A., Rees H., Quantitative Economic Policies and Interactive Planning, University Press, Cambridge 1983.
• [19] Kydland F., Decentralized Stabilisation Policies: Optimization and the Assignment Problem, Annals of Economic and Social Measurement 5, 1976, s. 249-261.
• [20] Kydland F., Noncooperative and Dominant Player Solutions in Discrete Dynamic Games, International Economic Review 16, 2, 1975, s. 321-335.
• [21] Miller M., Salmon M., Dynamic Games and the Time Inconsistency of Optimal Policy in Open Economies, Economic Journal, Supplement 95, 1985, s. 124-137.
• [22] Miller M., Salmon M., Policy Coordination and Dynamic Games, w: W. Buiter, R. Marston (wyd.) International Economic Policy Coordination, Cambridge University Press, Cambridge 1984.
• [23] Nash J., Non-Cooperative Games, Annals of Mathematics 54, 1951, s. 286-295.
• [24] Petit M.L., Control Theory and Dynamic Games in Economic Policy Analysis. Cambridge University Press, Cambridge 1990.
• [25] Pindyck R.S., Optimal Economic Stabilization Policies Under Decentralized Control and Conflicting Objectives, IEEE Transactions on Automatic Control AC-22, 1977, s. 517-530.
• [26] Pindyck R.S., The Cost of Conflicting Objectives in Policy Formulation, Annals of Economic and Social Measurement 5, 1976, s. 239-248.
• [27] Pindyck R.S., Optimal Planning for Economic Stabilization, North-Holland, Amsterdam 1973.
• [28] Pontriagin L.S., Boltianski V.G., Gamkrelidze R.V., Miszczenko E.F. (wyd.) The Mathematical Theory of Optimal Processes, John Wiley & Sons, New York 1972.
• [29] Selten R., Reexamination of the Perfectness Concept for Equilibrium Points in Extensive Games, International Journal of Game Theory 4, 1975, s. 25-55.
• [30] Simaan M., Cruz J.B., On the Stackelberg Strategy in Nonzero-Sum Games, Journal of Optimization Theory and Applications 11, 5, 1973a.
• [31] Simaan M., Cruz J.B., Additional Aspects of the Stackelberg Strategy in Nonzero-Sum Games, Journal of Optimization Theory and Applications 11, 6, 1973b.
• [32] Starr A.W., Ho Y.C., Non-Zero-Sum Differential Games, Journal of Optimization Theory and Application 3, 1969a, s. 184-206.
• [33] Starr A.W., Ho Y.C., Further Properties of Non-Zero-Sum Differential Games, Journal of Optimization Theory and Application 3, 1969b, s. 207-219.
• [34] Strzała K., Zastosowanie uogólnionych metod sterowania optymalnego do podejmowania decyzji gospodarczych, rozprawa habilitacyjna, Wydawnictwo Uniwersytetu Gdańskiego, Sopot 1994.
• [35] Strzała K., Nash Solution to the Conflict between Populists and Industrialists in Poland, w: Proceedings of XXXVIII th International Conference on Budgetary Policy Modelling. Public Expenditures, Atheny 13-14.04.1993.
• [36] Strzała K., Game Theoretical Approach to Optimal Control of Economic Systems, w: J. Gruber (wyd.) Econometric Decision Models. New Methods of Modeling and Applications. Proceedings of the Second Conference on Econometric Decision Models, University of Hagen, 29.08-01.09.1989, Lecture Notes in Economics and Mathematical Systems, vol. 366, Springer Verlag, Berlin 1991, s. 79-93.
• [37] Strzała K., Wybrane aspekty zastosowań teorii sterowania optymalnego w systemach ekonomicznych, w: Acta Universitatis Nicolai Copernici, Ekonomia XX, Toruń 1989, s. 107-118.