What is a Monte Carlo Simulation?

The Monte Carlo Method establishes a scenario bound by certain assumptions and probabilities. It then runs through a simulation of that scenario many times. At the end, an aggregation of the results of those simulations yields insight into the range of possible outcomes. In this case, we establish the probability of an event happening (conventional war, nuclear war, etc) and run through a set time period to simulate when that event might happen and what the associated costs might be.

How do you calculate Total Cost in each scenario?

To calculate the total cost of each scenario, the money spent on war and deterrence goes into a hypothetical fund to be used on public investment. The fund appreciates in value each year by the "alternative investment return" that you set. The value of that public investment fund at the end of your scenario is the total cost of war and deterrence. This methodology is superior to simply counting the dollars spent on defense because the time value of money matters. If the alternative investment return is greater than inflation, then it is in a nation's best interest to stave off war for as long as possible. If we simply added the nominal dollars spent on defense, we might conclude, incorrectly, that it is better to get war over with sooner.

Does the cost of war and deterrence stay constant or change over time?

The costs of war and deterrence increase at the defense-specific inflation rate that you set. The DoD establishes an inflation rate that is unique to its own purchases. This is the relevant rate, since we are talking about its purchases. What this simulator does not take into account is the potential scenario where delaying war allows an opponent to strengthen, and increase the cost of war.

What are some of the limitations of these tools?
One of the largest current limitations is the lack of an accounting of how deterrence might alter the cost of war, should it happen. On the one hand, we might think that if a nation prepares for war, it will perform better and final cost will be less. On the other hand, arms races have happened repeatedly over the course of history. It might be that increased defense spending will only force an adversary to better prepare themselves.

Another serious limitation is the singularity of the events. For example, in the terrorism simulation, we only consider counter-terrorism funds' impact on a 9/11 style attack. We ignore the benefits that spending brings in mitigating smaller terrorist attacks. This is done because the cost of smaller attacks is an order of magnitude smaller than those of a large attack. But it is still missing from the analysis. Similarly, in the nuclear war simulation, we might include a probabilities for an all-out war, a limited war, and a terrorist detonation.

Future iterations of these tools will explore these dynamics.