OPTIMAL ALLOCATION OF DRUG-CONTROL EFFORTS - A DIFFERENTIAL GAME ANALYSIS

The present paper considers a dynamic nonzero-sum game between drug de alers and the authorities. Although the game is neither linear-quadrat ic nor degenerate, in the sense that the closed-loop equilibria coinci de with the open-loop equilibria, we are able to calculate explicitly a stationary feedback Nash equilibrium of that game. In a numerical ex ample, we determine the optimal allocation of governmental efforts bet ween treatment and law enforcement minimizing the total discounted cos t stream in the equilibrium. Moreover, we provide sensitivity analyses with respect to the efficiency parameters of both competitors. Our re sults show that a farsighted authority should attack the drug problem from the demand side and put much effort in treatment measures and the improvement of the efficiency of the treatment.