Open-Loop Stackelberg Equilibrium Solutions of Differential Games and Dynamic Economic Rational-Expectations Models

Abstract

For a general linear-quadratic differential game model with two decision-makers, we characterize analytically the open-loop Stackelberg equilibrium solution. This can be interpreted as a model of macroeco-nomic policies, where the government acts as the leader and the private-sector agents act as followers in the game. On the other hand, we consider a linear multivariable dynamic economic system in continuous time, where economic agents have rational expectations with respect to some state variables. From a comparison of the two models, it becomes obvious that they are formally equivalent under some further assumptions. Some consequences of this result for the design of stabilization policies under rational expectations are briefly discussed.