I posted an interesting table from this paper a few weeks ago, showing the percentage of time the European great powers were at war by century.

Having now actually reviewed the paper's argument in depth, I can summarize it here.

Hoffman argues that for the rulers of European great powers from 1500 onwards, choosing to fight wars was similar to a tournament - it takes investment (here, military spending) and the winner gets a prize (territory, military prestige). This is also when gunpowder weapons emerge fully onto the scene. Gunpowder, unlike more conventional fighting methods with melee weapons or archery, has vast potential to be improved through dedicated research or improvement on past experience, called "learning by doing." He gives the latter more emphasis in the model:

One reasonable way to conceive of the learning is to assume that it depends on the resources spent on war. Greater military spending gives a ruler more of a chance to learn, and rulers anywhere can do it —it is not peculiar to one corner of the world. We can model the relationship by assuming that each unit of resources z spent gives a ruler an independent chance at a random military innovation x, where x has an absolutely continuous cumulative distribution function F(x) with support [0, a].

Emphasis mine. Essentially, spending more on war and fighting more gives you a better chance to learn to fight better. You can also copy others' innovations from previous rounds of warfare, allowing knowledge to disperse, although he allows for frictions in said dispersal later in the paper.

An important point he introduces is that gunpowder weaponry is not effective against every type of enemy. It works against conventional states with fixed populations and fortifications, but is less effective against nomadic armies without cities to beseige and which can continually retreat into their steppe. Western states primarily fought other equivalent centralized states, which was also the case in pre-Tokugawa era Japan, but China primarily fought against nomads, the Ottomans and the early Russian empire fought against a mix of states and nomads, and Indian warfare also featured such battles. These states will mix their spending on gunpowder and horse archer style forces depending on their threat mix. As horse archery holds less potential for improvement, states dependent upon it are prone to falling behind over time.

Skipping the boring model math, we reach some paragraphs worth quoting at length. His model predicts we will see sustained warfare and military development if:

(...) the value of the prize [of winning a war] is higher, when opponents’ costs ci [political costs of military spending] are similar, and when fixed costs b [fixed costs of setting up a fiscal system, military system, and navy] are smaller. Opponents’ costs will be similar if rival countries are of roughly the same size and face similar resistance to tax levies or conscription. The fixed costs will be small if setting up an army, a navy, or a fiscal system does not entail heavy expenses. That would certainly be the case if some of the fixed costs are sunk because a tax bureaucracy was already in place, naval dockyards had already been built, or a system had already been established for drafting soldiers, commandeering ships, or supplying provisions. The fixed costs would likely be modest too if the two rulers’ realms lay near one another, for fighting a distant country would entail setting up a big invasion force. War will persist if the inequality holds for successive generations of rulers.

Without war, there will be no learning by doing and no improvement in military technology. If the fighting halts, so will advances in military technology, and the resources mobilized zi will decline too. War will be likely to stop if the fixed costs rise, or if a ruler annihilates his opponents and conquers their realms. His successors will then have no nearby rivals, and their only potential adversaries will be further away and so entail larger fixed costs. It will simply not be worth fighting them.

This is a necessary, but not sufficient, condition for continued military innovation. Three other conditions are required:

The resources spent on warfare must be high, which is caused by having a large prize to win by fighting relative to political costs of fighting.

States must use gunpowder weaponry heavily, to ensure enough doing to cause learning by doing.

States must be able to acquire the latest innovations in gunpowder technology from other states at low cost.

He goes through why these conditions failed in various non-western regions.

All three conditions fail in China. It lacked suitable targets to take over; conquering Japan would have required the creation of a large enough navy, a very large fixed cost relative to the prize of conquest. It also fought primarily against nomads, leading to focus on non-gunpowder weaponry. Finally, acquiring many western military techniques such as the creation of modern artillery would have required recruiting large teams of highly-skilled military specialists from Europe, which would have been difficult and expensive.

Japan did see some continuous military development in its warlord phase, but once the Shogunate took over the country it ran into the same factors as China. A brief attempt to conquer Korea turned out to be extremely costly and was abandoned after its main leader died, serving as a sort of exception which proves the rule.

India had some nomad conflicts, splitting effort between weaponry types. As well, its low taxation rates, imply high political costs to taxation, leading to relatively low military spending. As well, dynastic strife within ruling families reduced the value of winning military glory, since a winning ruler might be assassinated by a relative, making his conquests pointless. These factors kept a lid on gunpowder-related military spending. The British East India Company could therefore roll up much of the subcontinent by taking advantage of its low cost to mobilizing military resources and exploiting succession crises.

Russia and the Ottoman Empire diverge partway through the period. Initially, both seem to have high costs of mobilizing resources to fight, and both are splitting their wars between western states and nomadic armies. However, once Russia conquers most of its nomadic enemies, and implements peasant conscription, it focuses more squarely on gunpowder weaponry with greater resources than before. So from around 1700, its fortunes diverge from the Ottoman Empire, and it starts performing better against European enemies while the Ottomans fall behind.

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Overall, an interesting paper. I'm sure that area experts would be driven to a blind fury seeing their region's fiscal realities simplified as "high costs of mobilizing resources," and pour out thousands of words arguing that lower Chinese tax revenues fail to reflect the true reality on the ground. But the use of even just a simple game theory model allows Hoffman to make his argument mathematically explicit, as opposed to a mushier wordy history argument with many fiddly points left for rhetorical wiggle room.

Historians should try to be more like this: