Clausewitz said it best - war is just politics executed with other means.
War starts when the cost/benefit analysis of violent means comes up better than the alternative (peaceful) means. War ends when the opposite happens, and the cost/benefit of the continuation of violence starts to come down in comparison with peace.
The benefit component is for the most part a zero-sum game (fixed land area), while the cost component is variable and growing with time. One way to force peace is to impose great costs on one or both warring sides.
That is not what Clausewitz said. He said that war is a paradoxical trinity of policy, rage, and chance, and that each war is a chameleon that takes on its own unique form.
More people like to glibly quote Clausewitz than have actually read and understood Clausewitz.
Goals are not rational. Neither Putin's goal of controlling Ukraine nor Ukraine's desire for independence are rational, they're subjective preferences.
You can ask - was Putin's decision to invade Ukraine rational given his values, priorities, risk aversion, willingness to bear the costs and information he had? Apart from the last, they're all subjective and thus it doesn't make sense to judge them as (ir)rational. The last one is objective, but having wrong information is not irrational either.
Some people just want to fight. As a goal by itself. Sure you can say that if they want to fight, fighting is the rational choice, but that definition would make every action 'rational'.
> Some people just want to fight. As a goal by itself.
Can you make some examples of war where fighting itself was the primary goal?
> that definition would make every action 'rational'.
As mentioned above, goals themselves are not something we can evaluate as rational or not.
But given you have a goal, you can question whether the actions you undertake to achieve that goal are rational. Let's say you want to start a family and want to buy a house. Going into a casino and throwing money into the slot machines is not a rational way to achieve it, esp. since there is plenty of information available explaining in painstaking detail that this won't work.
Can you make some examples of war where fighting itself was the primary goal?
It's possible that we're seeing one now in Ukraine. The Russian army isn't exactly made up of economic elites, being composed largely of men from outlying territories who are either a possible long-term threat to Putin's vision of Soviet-era revanchism or impoverished people who are literally more trouble to feed than they're worth. From Putin's point of view, a meat grinder may be just what the (mad) doctor ordered.
Certainly that dovetails with Kim's motivation to send his own hungry soldiers to the Ukraine front. Now that he has nukes, what does he need such a large army for? Like the ragtag derelicts and criminal elements who make up the Russian armed forces, those troops are more of a liability to Kim than an asset.
See also concerns about China's surplus of young men who will never find mates thanks to the effects of the regime's one-child policy. A literal incel army. It's not hard to imagine that Beijing might find a war to be a convenient way to rebalance the population and remove a potential source of agitation.
Even in the scenarios you describe, the wars would be based on political goals (even if the goal is killing your own citizens by sending them to war), not because anyone is "wanting to fight". Very different things.
War starts when the cost/benefit analysis of violent means comes up better than the alternative (peaceful) means. War ends when the opposite happens, and the cost/benefit of the continuation of violence starts to come down in comparison with peace.
The benefit component is for the most part a zero-sum game (fixed land area), while the cost component is variable and growing with time. One way to force peace is to impose great costs on one or both warring sides.