Obama is close to a decision on the U.S. strategy is Afghanistan.  What is the rational way to approach this decision assuming the U.S. is maximizing its own payoff?  This is the “realist” assumption rather than one incorporating a moral component, though it is not too hard to jazz up some of the analysis to deal with this objective function too.

First, think through whether we should be there in the first place.  What is the threat to the U.S. if Afghanistan falls to the Taliban?  Will Al Qaeda move back in or not?  If the belief is that the Taliban is not a threat to the U.S. and Al Qaeda will not move in, the realist conclusion is to withdraw and focus on counterterrorism.  This is the debate taking place within the Obama adminstration

Second, what if the Taliban is a threat and/or Al Qaeda will flourish in a Taliban-led Afghanistan?  This is the more interesting case from the strategic perspective and an analysis has been provided by Nolan Miller.  He applies it to Iraq as his paper was written during the election but it could equally be applied to Afghanistan.

The U.S. strategy affects two other players, Karzai and the Taliban.  If the U.S. adopts an aggressive approach and commits to a large military presence, this reduces the incentive of the Taliban to be aggressive and their effort is more likely to be futile.  But equally there is a free rider problem for Karzai: if the U.S. is exerting effort anyway, this reduces the incentive of Karzai to do so.

These two effects go in opposite directions.  If Karzai is weaker than the Taliban in the absence of intervention, the reduction in his effort after U.S. intervention is outweighed by the reduction in the effort of the Taliban.  In that case, it is better to adopt an “output-based” strategy where the U.S. commits to a security level that it tries to achieve regardless of the Karzai government’s and insurgent’s effort.

This appears to be the pertinent case if  the belief is that we should pursue counterinsurgency rather than counterterrorism.  Miller also explores more complex solutions.