This is meant for fellow economists. In our fight against problems like illegal drug use or terrorism, we’d like to analyze if some corrective measures would lead us to “win the war on drugs or terror.”  How do we theoretically define winning or losing in such a context? 

My 2021 published paper with Sajal Lahiri, Why direct counter-terrorism measures only may fail: An analysis of direct and preventive counter-terrorism measures in the International Journal of Economic Theory suggests the following.

Let the parameter, say ‘a’ represent the original, exogeneous, state of drugs or terrorism, ‘m’ denote the level of corrective measures chosen rationally by the state by weighing the costs and benefits, given ‘a’, and let the associated equilibrium level of damage be ‘d’.  Thus, ‘d’ should increase with ‘a’ and decrease with ‘m’.

Now let a increase to a level ‘A’ and denote the worsening of the problem due to exogeneous reasons. This will lead to an equilibrium increase in m say to ‘M’.  Let ‘D’ be the corresponding equilibrium level of damage. Compared to dD would tend to be higher because of the exogenous increase in the problem but tend to be lower because of an increase in the corrective measures m

The Definition

We then define that the war on drugs or terrorism is won if D is less than d or weakly won if D = d.

It means that if the rational increase in the corrective measures in response to an exogenous, initial, increase in the problem is such that the damage from the problem is less than before, the war is won.

Otherwise, if D > d, the increase in the corrective measure is not large enough to reduce the damage.  Hence the war is lost.

An Example in the Context of Terrorism

Using this definition, Sajal Lahiri and I have shown that terrorism cannot be won by preemptive measures if the marginal cost of preemptive measures for the state is increasing.