The Optimal Number of MDP's
Entry posted by Ferrous
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Introduction
Some alliances think that the more Mutual Defense Pacts (MDPs), and their cousin, the MDoAP*, the more secure they are. However, when two alliances form an MDP, there is a certain amount of baggage** that each alliance brings along with them. This extra baggage can increase the chances of an alliance to be engaged in war. Additionally, depending on the size of the alliance, the MoFA can handle working with so many allies at once. So hence, there is a point where there is such a thing as too many MDPs. However, the real question is, "is there an optimal amount of MDP's?" The answer that I endeavor to explain is, yes, there is.
Increase in War
Let us suppose that two alliances, A and B decide to form a mutual defense pact. Wonderful. To some, this may serve as a deterrent for war. However, since any rival alliances will surely have pacts of their own, and it is likely that both alliances A and B are now linked to the MDP-web***, it is also now more likely that either one or both of the alliances will be dragged into a war that neither one of them initially started. Assuming a linear increase in the percentage of wars over time as a function of the number of agreements for an alliance, we have the following graph:
Increase in Military Effectiveness
Additionally, for every mutual defense pact signed, there is an increase in military effectiveness, but one that has diminishing marginal returns. Imagine that alliance A signed its very first mutual defense pact. It is now twice as strong as it was before (roughly), and since its pact is its first pact, it is relatively easy to coordinate military operations with just the two alliances. Now suppose that alliance A signs a second pact: there is a comparable increase in military strength, but the operations are not quite as well coordinated, so its not as effective as the first pact signed. As the pattern continues, we see that each MDP signed will grant smaller and smaller amounts of military effectiveness. In fact, we eventually can come to the point where it is not beneficial to sign an MDP, since there will be too many coordination issues, and the status of each MDP will be diminished (since there is no "best friend" any more). We can illustrate this concept with the following graph:
The MDP Saturation Model
Now, let us superimpose these graphs on top of each other. We get the following:
A couple of interesting points, namely A, B, and C. Note how the PIME (Percent Increase in Military Effectiveness) is larger than the PINW (Percent Increase in the Number of Wars) up until point B. This would mean that until point B, an alliance can continually sign pacts with other alliances until the cons of being engaged in war would eventually catch up. At point B, it is no longer beneficial to sign another pact, since the cons (measured in percent increase in wars) would outweigh the pros (measured in the military benefit of each alliance). Additionally, note point A - this is the point where the slope of the PINW and the PIME are equal (or as best I could make out). Why is this significant? This point could be interpreted as the "optimal number of MDP's", where the distance between the PINW and the PIME is greatest (anyone with a background in calculus can confirm this).
At this point, it is probably impossible to measure exactly where points A and B are. However, using these graphs, it should become clear that there is a point where MDP's each have their maximum amount of benefit that they provide, as well as a point where there is such thing as too many MDP's. Also, you may be wondering where Blocs fit into this analysis; blocs, by their nature, share much of the same baggage, so the increase in number of wars is greatly diminished with a new signatory, since the wars that the new signatory would be fighting are likely to be the same wars as the rest of the bloc would be fighting. Additionally, since blocs work together and have solutions to coordination issues built in, they do not experience the same rate of diminishing marginal returns as a regular MDP would.
Hopefully this model will give some insight to how the number of MDP's is determined, and how many we can expect to see in the future.
Notes:
*Mutual Defense, optional Aggression Pact
**In the form of rivalries, obligations to other alliances, etc.
***Term used to describe the vast number of intertwining alliance agreements
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