Existence and Policy Effectiveness in Feedback Nash LQ-Games

Nicola Acocella, Giovanni Di Bartolomeo

Abstract


This paper illustrates how the classical theory of economic policy can profitably be used to verify some properties of the Linear Nash Feedback Equilibrium in difference LQ-games. In particular, we find that both a necessary condition for the equilibrium existence and a sufficient condition for policy ineffectiveness can be defined in the terms of the simple Tinbergen counting rule.


Keywords


LQ-policy games, policy ineffectiveness, controllability, Linear Feedback Nash Equilibrium existence.

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References


Aarle, B. van, A.L. Bovenberg, and M.G. Raith (1997), “Is There a Tragedy for a Common Central Bank? A Dynamic Analysis,” Journal of Economic Dynamics and Control, 21: 417-447.

Acocella, N. and G. Di Bartolomeo (2004), “Non-Neutrality of Monetary Policy in Policy Games,” European Journal of Political Economy, 20: 695-707.

Acocella, N. and G. Di Bartolomeo (2006), “Tinbergen and Theil Meet Nash: Controllability in Policy Games,” Economics Letters, 90: 213-18.

Acocella, N., G. Di Bartolomeo, and A. Hughes Hallett (2007), “Dynamic Controllability with Overlapping Targets: Or Why Target Independence May Not Be Good for You,” Macroeconomic Dynamics, 11, 202-213.

Aoki, M. (1975), “On a Generalization of Tinbergen’s Condition in the Theory of Policy to Dynamic Models,” Review of Economic Studies, 42: 293-296. Başar, T. and G.J. Olsder (1995), Dynamic Noncooperative Game Theory, second edition, Academic Press Limited, London.

Başar, T., V. D’Orey, and S.J. Turnovsky (1988), “Dynamic Strategic Monetary Policies and Coordination in Interdependent Economies,” American Economic Review, 78: 341-61.

Dasgupta, P. and E. Maskin, (1986), “The Existence of the Equilibrium in Discontinuous Economic Games. I: Theory,” Review of Economic Studies, 53: 1-26.

Di Bartolomeo, G., J.C. Engwerda, J. Plasmans, B. van Aarle, and T. Michalak (2006),“Macroeconomic Stabilization Policies in the EMU: Spillovers Asymmetries and Institutions,” Scottish Journal of Political Economy, 53: 461-483.

Dockner, E., S. Jorgensen, N. Van Long, and G. Sorger (2000), Differential Games in Economics and Management Sciences, Cambridge University Press, Cambridge.

Engwerda, J.C. (2000a), “Feedback Nash Equilibria in the Scalar Infinite Horizon LQ-game,” Automatica, 36: 135-139.

Engwerda, J.C. (2000b), “The Solution Set of the N-Player Scalar Feedback Nash Algebraic Riccati Equations,” IEEE Transactions on Automatic Control, 45: 2363-2369.

Engwerda, J.C. (2006), “Linear Quadratic Differential Games: An Overview,” University of Tilburg, CentER Discussion Paper No. 110.

Engwerda, J.C., B. van Aarle, and J. Plasmans (2002), “Cooperative and Non-Cooperative Fiscal Stabilisation Policies in the EMU,” Journal of Economic Dynamics and Control, 26:

-481.

Fujiwara K. and N. Matsueda (2007), “On a Nonlinear Feedback Strategy Equilibrium of a Dynamic Game,” Economics Bulletin, 3, No. 8.

Gylfason, T. and A. Lindbeck (1994), “The Interaction of Monetary Policy and Wages,” Public Choice, 79: 33-46.

Ljungqvist L. and T. Sargent (2004), Recursive Macroeconomic Theory, second edition, The MIT Press, Cambridge.

Levine, P. and A. Brociner (1994), “Fiscal Policy Coordination and EMU,” Journal of Economic Dynamics and Control, 18: 699-729.

Levine, P. and R. Smith (2000), “The Arms Trade Game: from Laissez Faire to a Common Defence Policy,” Oxford Economic Papers, 52: 357-380.

Lucas, R.E. (1976), “Econometric Policy Evaluation. A Critique,” Journal of Monetary Economics, Supplement, Carnegie-Rochester Conference Series on Public Policy, 1: 19-46.

Neck, R. and E.J. Dockner (1995), “Commitment and Coordination in a Dynamic Game Model of International Economic Policy-Making,” Open Economies Review, 6: 5-28.

Pappa, E. (2004), “Do the ECB and the Fed Really Need to Cooperate? Optimal Monetary Policy in a Two-Country World,” Journal of Monetary Economics, 51: 753-779.

Plasmans, J., J.C. Engwerda, B. van Aarle, G. Di Bartolomeo, and T. Michalak (2005), Dynamic Modeling of Monetary and Fiscal Cooperation Among Nations, Springer, Berlin.

Preston, A.J. (1974), “A Dynamic Generalization of Tinbergen’s Theory of Policy,” Review of Economic Studies, 41: 65-74.

Sargent, T.J. (1987), Dynamic Macroeconomic Theory, Harvard University Press, Cambridge.

Tsutsui, S. and K. Mino (1990), “Nonlinear Strategies in Dynamic Duopolistic Competition with Sticky Prices,” Journal of Economic Theory, 52: 136-161.


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