Macroeconomic Stabilization Policies in the EMU: Spillovers, Asymmetries, and Institutions

This paper studies the institutional design of the coordination of macroeconomic stabilization policies within a monetary union in the framework of linear quadratic differential games. A central role in the analysis plays the partitioned game approach of the endogenous coalition formation literature. The specific policy recommendations in the EMU context depend on the particular characteristics of the shocks and the economic structure. In the case of a common shock, fiscal coordination or full policy coordination is desirable. When asymmetric shocks are considered, fiscal coordination improves the performance but full policy coordination doesn’t produce further gains in policymakers’ welfare.macroeconomic stabilization, EMU, coalition formation, linear quadratic differential games

A Simulation Study of an ASEAN Monetary Union (Replaces CentER DP 2010-100)

This paper analyzes some pros and cons of a monetary union for the ASEAN1 countries, excluding Myanmar. We estimate a stylized open-economy dynamic general equilibrium model for the ASEAN countries. Using the framework of linear quadratic differential games, we contrast the potential gains or losses for these countries due to economic shocks, in case they maintain their status-quo, they coordinate their monetary and/or fiscal policies, or form a monetary union. Assuming for all players open-loop information, we conclude that there are substantial gains from cooperation of monetary authorities. We also find that whether a monetary union improves upon monetary cooperation depends on the type of shocks and the extent of fiscal policy cooperation. Results are based both on a theoretical study of the structure of the estimated model and a simulation study.ASEAN economic integration;monetary union;linear quadratic differential games;open-loop information structure

Algorithms for Computing Nash Equilibria in Deterministic LQ Games

In this paper we review a number of algorithms to compute Nash equilibria in deterministic linear quadratic differential games.We will review the open-loop and feedback information case.In both cases we address both the finite and the infinite-planning horizon.Algebraic Riccati equations;linear quadratic differential games;Nash equilibria

Magnus integrators for solving linear-quadratic differential games

We consider Magnus integrators to solve linear-quadratic N-player differential games. These problems require to solve, backward in time, non-autonomous matrix Riccati differential equations which are coupled with the linear differential equations for the dynamic state of the game, to be integrated forward in time. We analyze different Magnus integrators which can provide either analytical or numerical approximations to the equations. They can be considered as time-averaging methods and frequently are used as exponential integrators. We show that they preserve some of the most relevant qualitative properties of the solution for the matrix Riccati differential equations as well as for the remaining equations. The analytical approximations allow us to study the problem in terms of the parameters involved. Some numerical examples are also considered which show that exponential methods are, in general, superior to standard methods.The authors acknowledge the support of the Generalitat Valenciana through the project GV/2009/032. The work of SB has also been partially supported by Ministerio de Ciencia e Innovacion (Spain) under the coordinated project MTM2010-18246-C03 (co-financed by the ERDF of the European Union) and the work of EP has also been partially supported by Ministerio de Ciencia e Innvacion of Spain, by the project MTM2009-08587.Blanes Zamora, S.; Ponsoda Miralles, E. (2012). Magnus integrators for solving linear-quadratic differential games. Journal of Computational and Applied Mathematics. 236(14):3394-3408. https://doi.org/10.1016/j.cam.2012.03.008S339434082361

Parameter identification applied to linear quadratic differential games

A two player zero-sum linear quadratic differential game is investigated for the case in which one of the players has incomplete a priori knowledge of the parameters of his opponent\u27s dynamic system. This incomplete system parameter information game is shown to be playable since the ignorant player can make limiting estimates of the unknown parameters from the relative controllability condition for the game. Performance from the ignorant player\u27s point of view is suboptimal. It is also shown that parameter identification techniques can be applied by the ignorant player in order to directly identify the smart player\u27s closed-loop parameters in the case in which the smart player\u27s optimal control gains become time-invariant. The open-loop system parameters may then be estimated from the identified closed-loop parameters. Using these estimated open-loop parameters in the optimal control law results in an asymptotically optimal adaptive control strategy for the ignorant player. Both continuous and discrete time parameter identification techniques were applied to the incomplete system parameter information game. In doing so, multivariable extensions were derived for previously developed single input/output continuous time and discrete time identification techniques. A multivariable combination response error and equation error continuous time learning model identification technique was also developed --Abstract, page ii

Numerical approaches to linear—quadratic differential games with imperfect observations

A two-person pursuit—evasion stochastic differential game with state and measurements corrupted by noises is considered. In an earlier paper the problem was reformulated and solved in an infinite-dimensional-state space, and the existence of saddle-point solutions under certain conditions was proved. The present paper provides a numerical solution for the resulting continuous-time integro-partial differential equations. This solution scheme is based on the utilization of the second guessing technique, and, in spite of the fact that a complicated set of integro-partial differential equations have to be solved, the numerical results seem plausible and promising