On the open-loop Nash equilibrium in LQ-games

Journal of Economic Dynamics and Control

Volumn 22, Issue 5, 1998, Pages 729-762

  Engwerda, Jacob C ^a  

^a TILBURG UNIVERSITY   (Netherlands)

Author keywords

Linear quadratic games; Open loop Nash equilibrium; Riccati equations; Solvability conditions

Indexed keywords

EID: 0032065686     PISSN: 01651889     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0165-1889(97)00084-5     Document Type: Article

References (30)

1. Aarle, B. van, Bovenberg, L., Raith, M., 1995. Monetary and fiscal policy interaction and government debt stabilization. Journal of Economics 62(2) 111-140.
2. Abou-Kandil, H., Bertrand, P., 1986. Analytic solution for a class of linear quadratic open-loop Nash games, International Journal of Control 43, 997-1002.
3. Abou-Kandil, H., Freiling, G., Jank, G., 1993. Necessary and sufficient conditions for constant solutions of coupled Riccati equations in Nash games; Systems and Control Letters 21, 295-306.
4. Başar, T., Olsder, G.J., 1982. Dynamic Noncooperative Game Theory. Academic Press, London.
5. Dockner, F.G., Jørgensen, S., 1985. Tracktable classes of nonzero-sum open-loop Nash differential games. Journal of Optimization Theory and Applications 45(2) 179-197.
6. Douven, R.C., Engwerda, J.C., 1995. Is there room for convergence in the E.C.?, European Journal of Political Economy 11, 113-130.
7. Eisele, T., 1982. Nonexistence and nonuniqueness of open-loop equilibria in linear-quadratic differential games. Journal of Optimization Theory and Applications 37. In: Isidori, A. (Ed.), 443-468.
8. Engwerda, J.C., Weeren A.J.T.M., 1994. On the inertia of the matrix (matrix presented). In: Breton, M., Zaccour, G. (Eds.) Preprint volume Sixth International Symposium on Dynamic Games and Applications. St. Jovite, Québec, Canada, GERAD Ecole des H.E.C., Montréal, Canada, pp. 565-571.
9. Engwerda, J.C., Weeren A.J.T.M., 1995. On the solutions of the algebraic Riccati equation corresponding to the open-loop Nash equilibrium in LQ-games, In: Isidori, A. (Ed.), Proceedings of the third European Control Conference, University of Rome "La Sapienza", pp. 2615-2619.
10. Engwerda, J.C., 1996. Open-loop Nash equilibria in the infinite-planning horizon LQ-game, In: Bańka, S. (Ed.) Proceedings of third MMAR Conference, Technical University of Szczecin, Poland, pp. 257-262.
11. Fershtman, C., Kamien I., 1987. Dynamic duopolistic competition with sticky prices, Econometrica 55, 1151-1164.
12. Feucht, M., 1994. Linear-quadratische Differentialspiele und gekoppelte Riccatische Matrixdifferentialgleichungen, PhD. Thesis, Universität Ulm, Germany.
13. Friedman, A., 1971. Differential Games, Wiley, New York.
14. Halkin, H., 1974. Necessary conditions for optimal control problems with infinite horizons. Econometrica 42, 267-272.
15. Haurie, A., Leitmann G., 1984. On the global asymptotic stability of equilibrium solutions for open-loop differential games. Large Scale Systems 6, 107-122.
16. Kaitala, V., Pohjola M., Tahvonen O., 1992. Transboundary air polution and soil acidification: a dynamic analysis of an acid rain game between Finland and the USSR. Environmental and Resource Economics 2, 161-181.
17. Lancaster, P., Tismenetsky M., 1985. The Theory of Matrices. Academic Press, London.
18. Levine, P., Brociner A., 1994. Fiscal policy coordination and EMU: a dynamic game approach. Journal of Economic Dynamics and Control 18, 699-729.
19. Lukes, D.L., Russell D.L., 1971. Linear-quadratic games. Journal of Mathematical Analysis and Applications 33, 96-123.
20. MacFarlane, A.G.J., 1963. An eigenvector solution of the optimal linear regulator. Journal of Electronic Control 14, 643-654.
21. Mäler, K.-G., 1992. Critical loads and international environmental cooperation. In: Pethig, R. (Ed.), Conflicts and Cooperation in Managing Environmental Resources, Springer Berlin.
22. Meyer, H.-B., 1976. The matrix equation AZ + B - ZCZ - ZD = 0. Siam Journal Applied Mathematics, 30(1), 136-142.
23. Neck, R., Dockner E.J., 1995. Commitment and coordination in a dynamic game model of international economic policy-making. Open Economies Review 6, 5-28.
24. Petit, M.L., 1989. Fiscal and monetary policy co-ordination: a differential game approach. J. Appl. Econometrics 4, 161-179.
25. Potter, J.E., 1966. Matrix quadratic solutions. SIAM Journal of Appllied Mathematics 14, 496-501.
26. Simaan, M., Cruz J.B., Jr., 1973. On the solution of the open-loop Nash Riccati equations in linear quadratic differential games. International Journal of Control 18, 57-63.
27. Starr, A.W., Ho Y.C., 1969. Nonzero-sum differential games. Journal of Optimization Theory and Applications 3, 184-206.
28. Tabellini, G., 1986. Money, debt and deficits in a dynamic game. Journal of Economic Dynamics and Control 10, 427-442.
29. Weeren, A.J.T.M., 1995. Coordination in Hierarchical Control. PhD. Thesis, Tilburg University, The Netherlands.
30. de Zeeuw, A.J., van der Ploeg F., 1991. Difference games and policy evaluation: a conceptual framework. Oxford Economic Papers 43, 612-636.