How Should Control Theory Be Used to Calculate a Time-Consistent Government Policy?

The authors study different solutions to a simple one-dimensional linear qua dratic game with a large number of private agents and a government. A "time-consistent" solution is defined as a solution to the Hamilton- Jacobi-Bellman equation, i.e., as a policy for which the government has no precommitment capability. This solution is compared to a poli cy where the government has an "instantaneous" precommitment, i.e., an equilibrium in which the government has a period by period leader ship. In both cases, the authors show how control theory should be ap plied to calculate the equilibrium and how to relate these equilibria to the differential game literature. Copyright 1988 by The Review of Economic Studies Limited.