We will deal with the trivial case first. If two nations are both using non-POM monies they cannot go to war because no one would be paid for engaging in a war of aggression. There is no net benefit from starting a war for any of the participants. There is lots of money to be made from preventing a war and from restraining others from starting a war. Finally, two such nations would be making lots of money by trading with each other and the citizens of each nation would want to continue that relationship to keep the money appearing in their accounts.
This brings us to that case of a POM nation relationship with a non-POM nation. Obviously, the POM nation has nothing to fear from the non-POM nation attacking them since there is no profit (net benefit) to be had by a war of invasion by the non-POM nation. Giving the orders to invade another nation would result in the orders being ignored and the author of those orders being restrained as mad or corrupt.
Therefore the only kind of war that might come about between a POM nation and a non-POM nation would be the case of the POM nation invading the non-POM nation. In such a case, the non-POM nation would benefit by expelling the invaders. It is obvious that the people who pay in the non-POM society would pay for the defense of their nation against attack.
Now I have not yet written the non-POM and Bureaucracy article since that title is unlikely to get many readers but I can say with considerable confidence that bureaucracies in a non-POM society are much more efficient and productive than those in a POM society because in a non-POM bureaucracy the workers are working with each other while in a POM bureaucracy the employees are working for their employers. This makes a huge difference. Also, each and every worker from the CEO (yes the CEO is also just a worker to those who pay) to the least skilled worker, is paid based on the consequences of his or her actions. Therefore the quality of the work is high and cooperation to make things better is rewarded. Poorly performing workers are asked to leave by the other workers. Those who don't "pull their weight" are encouraged to do better. The result is that the military bureaucracy of the non-POM nation will be much more efficient and effective than the invading POM military bureaucracy.
The equipment available to the non-POM military will be of superior quality to that of the POM military since the production bureaucracies of the non-POM factories and such will be much more efficient and productive than the POM production bureaucracies. The non-POM workers will be paid on the basis of how good the weapons and protective devices and so on are rather than by the hour for time at the machine. The "back room boys" who come up with new kinds of weapons will be much more effective and quicker to develop ideas for equipment since they will be sharing ideas and helping each other rather than keeping their ideas to themselves to maximize profit.
The officers in the non-POM military will be of better quality since they are a product of the better bureaucracy and its "free market" selection process for those who lead. (Yes, that's another article to come.)
Therefore, there is every chance that the non-POM military would quickly defeat the military of the invading POM nation unless the size difference in the militaries was huge.
But it requires considerable preparations on the part of a military organization before launching an invasion. The scale of such an activity is so large that it cannot be hidden. Thousands of people must participate in the preparations so it cannot be kept secret.
Therefore, the non-POM nation must be able to discover that an invasion might be in preparation. Upon discovering the threat, the non-POM nation has many options as to how to stop such a threat. They all revolve around the fact that the POM state will have a centralized authority which expects to benefit (there's that POM again) from an invasion. In order to stop the invasion the non-POM nation can use any technique which makes it clear to the rulers of the POM nation that they will personally lose heavily in the event of an invasion regardless of what their armies do. This could include assassination or threats to their wealth or support for their rivals in the government. You will have noticed that POM governments are always in fear of losing their powers to rivals within the government. If properly conducted, such operations could prevent a likely threat from ever coming to power in the first place. But whoever does prevent the invasion would be assured of major rewards from the payers. This would be like a standing reward offer to literally anyone, whether a citizen of the non-POM nation or not, who took action to prevent the invasion. Military leaders in the invading army would be aware of that of course. Could they resist the temptation to "take a bribe?" Would assassination replace war as a means of stopping aggressor nations? Would the POM leaders be willing to risk being killed or overthrown if they prepared to invade a non-POM nation? Remember that the non-POM nation simply by virtue of the nature of its money would create this situation for the POM invaders. They would not have to decide upon assassination or rewards for POM nation treason or for overthrowing an aggressive nation's leaders. Their money would provide that context for any aggressive nation. It would be automatic.
The obvious conclusion is that wars involving non-POM nations would be exceedingly rare and if there were any such wars the POM nations involved would change leaders soon and the war would be brief. This might be hard on the dictators of the world but it would take a considerable load off the innocent bystanders of the world.