The (in)finite horizon open-loop Nash LQ game: An application to EMU

In this paper, we study macroeconomic stabilization in the Economic and Monetary Union (EMU) using a dynamic games approach. In modeling this problem, it turns out that the players include the time derivative of the state variable of the game in their performance criterion. As far as the authors know, this kind of problem has not before been dealt with rigorously in dynamic games theoretic literature. Therefore, we first consider a generalization of the linear-quadratic differential game, in which we allow for cross terms in the performance criteria. Following the analysis of Engwerda [10,12], we present formulas to calculate open-loop Nash equilibria for both the finite-planning horizon and the infinite-planning horizon. Particular attention is paid to computational aspects. In the second part of this paper, we use the obtained theoretical results to study macroeconomic stabilization in the Economic and Monetary Union (EMU).