Cooperative and Non-Cooperative Solutions for a Linear- Quadratic Differential Game Model of Stabilization Policies

Abstract

A simple linear dynamic macroeconomic model of the trade-off between unemployment and inflation is considered. Two policy-making institutions, namely the government and the central bank, can exert influence on this economic system, aiming at reducing the rates of unemployment and of inflation by fiscal and monetary policies, with quadratic costs attached to the use of the respective own control variables; in addition, they give different weights to the target variables, which arc assumed to enter linearly into the objective functions. We solve the resulting linear-quadratic differential game both for the non-cooperative feedback Nash solution and for the set of Pareto-optimal solutions. It is shown that both solutions lead to constant strategies over the entire infinite time horizon. In the non-cooperative case, open-loop Nash, feedback Nash, and Stackelberg equilibria coincide. On the other hand, they do not belong to the set of Pareto-optimal outcomes and are therefore inefficient. Sensitivity analyses are provided for the optimal non-cooperative and cooperative strategies.

Helpful comments by an anonymous referee and financial support by the Hochschuljubiläumsstiftung der Stadt Wien are gratefully acknowledged.