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

Daniel Cohen and Philippe Michel

The Review of Economic Studies, 1988, vol. 55, issue 2, 263-274

Abstract: We study different solutions to a simple one-dimensional linear quadratic 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 noprecommitment capability. This solution is compared to a policy where the government has an "instantaneous" pre-commitment, i.e. an equilibrium in which the government has a period by period leadership. In both cases, we show how control theory should be applied to calculate the equilibrium and how to relate these equilibria to the differential game literature.

Date: 1988
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