@icekatze
I second that. There was a really interesting experiment where an amount of money was given to two people with their powers being as followed: The first decided the division of the money while the second could veto the entire thing, causing both to get nothing.
What happened is that on average the first had to offer the second at least 25%, otherwise the second would veto. This doesn't seem wrong to us emotionally and we might do the same, but mathematically we should be glad if we're even offered a penny, as we've come out richer than when we started.
It's the price of Pride.
However,
Realpolitik is a very real thing and numerous leaders have played the numbers like the protagonists to make things work out. The idea of making it just too costly and with too little gains to take a country was (and still is) done by Switzerland. Their entire country is equipped to be turned into a fortress and their entire infrastructure is set up to be destructible, making the country hard to take and worthless when you do.
On another topic: I don't like what they did to Lanchester's law. First of all, it has a form for ancient battles with spears and such. It's linear then, not squared as it is with guns. The reason is how Lanchester's law works. It's not a strategic formula, it's an engagement formula that goes by attrition.
Lanchester's law roughly works on the assumptions that guns make most other considerations, besides who has the most guns, inconsequential. So that number alone is needed for calculating the force value. It also assumes that unequal forces will become more and more unequal as the fight goes on. So if you have 30 men vs 10 and every 10 men kill one every one unit of time. After one you have 29(30) v 7(10) followed by 28.3(30) v 5.1(10), 27.79(30) v 2.4(10), before total annihilation. That compounding effect is why you should
square the numbers
not multiply the weapon effectiveness with the number of weapons.
Lanchester put this as a linear function when it comes to melee weapons because a single soldier can only ever engage one other soldier with a melee weapon, while that is not true for guns.
Finally, I've got a bad feeling about guns in this series. I was sure we were going to see something set in the early gunpowder age, given the guns, but they just said both armies are armed with spears. Even during the early gunpowder age the gun had become a massive part of armies. Armies still used pikes with pike and shot becoming the mainstay tactic of early fireweapons, but
then the author would have mentioned guns as well. Not to mention that early guns were horribly inaccurate due to not being rifled. My bad feeling is that the author forced guns into the story only for the sake of the classic game-theory gunmen scenario and is going to relegate them to something of a ornamental weapon, not deal with their massive accuracy (it was that accuracy as well as bayonets that led to the pike being completely abandoned. A pike was needed because a gun was worthless as a melee weapon and because the lack of range due to accuracy meant that you didn't have enough shots to efficiently deal with an enemy force) and start losing the thinking part of the manga (which is the brunt of it) due to lack of planning and thought going into it.