First Update Observations
I'm not going to do one of these for every update, but let's take a look at the worldstate through the eyes of our enemies here. Interesting things to note:
1) The jounin who survived our initial altercation are said to have fled back to Mist, rather than trying to go to ground. This indicates a very high belief in Mist's willingness to spare them in exchange for information. Common sense would say that Mist loses little from simply capturing these jounin, torturing them for information, and disposing of them. Especially since the jounin were already discarded from Mist's useful roster. I can't think of a non-convoluted reason why the survivors would undertake this course of action, especially since during the trek back to Mist they'll have time to think through the consequences of their "plan." Even more since the survivors fled at the end of the battle, and Shikigami didn't explain his plan until several minutes after the battle was over (things had calmed down enough for him to care about cosmetic stuff like blood on his hands, which means higher-priority tasks like checking for evasdroppers would have already been conducted).
We know this is a reasonable universe, which means that the GMs won't retroactively edit stuff to make things easier, but neither will they retroactively edit stuff to make things harder. Things are as they are, just as physics ran uninterrupted without human observers for 14 billion years. We think those shinobi fled to inform Mist, but it's possible that they, upon reflection, decided the more rational play was to go to ground and take the small possibility of survival vs the almost certain possibility of torture and death. Of course, we wouldn't know either way, but it would impact the size of our lead.
Note that running back to Mist, even if Mist lets them live, means they will almost certainty suffer extreme torture just to make sure their information is accurate and thorough. Even jounin in a realistic Narutoverse are not perfect stoic agents capable of unflinchingly contemplating the prospect of guaranteed torture. Even jounin are not immune to the heuristic which vastly overweighs immediate and guaranteed rewards over long-term and uncertain ones. Going to Mist, they will be tortured immediately, and they might someday live a life worth suffering through that. But it's extremely unlikely.
2) Remember, as much as we are constructing our projections from a position of relative ignorance, so are they. Search is an incredibly labor- and power-intensive task, because the difficulty of search scales with the square of the time elapsed. This is a simple consequence of constant search radius per person versus exponentially increasing potential area to be searched. Shinobi have strong incentives to develop both chakra-assisted tracking and chakra-assisted evasion, so it's likely that standard capabilities in these two fields are relatively evenly matched, with the decisive factor being the individual skill/ingenuity of the specific participants in question, plus circumstantial factors (more time = harder for search, unfamiliar enviroment = harder for search, etc).
3) Consider the hypothetical perspective of the Konoha rangers who chased us around before we entered the swamp. If we were playing them, we wouldn't know that the Mist-nin intend to settle down in the swamp. We wouldn't even know if they intended to make camp in the swamp, or stop at all, or whether it was simply a tactic to throw off pursuit. Maybe the jounin in that party just wanted a way to kill off all the dead-weight chunin and genin without a fight. If over the course of the next few days/weeks we don't see any conclusive sign of their party leaving the swamp (assuming our superiors in Konoha actually think it's worth the cost of extended search and deployment to this remote hellhole), that could mean either:
A) they all died inside, the crazy fools, or
B) they're somewhere in the swamp, possibly in some underwater base, or
C) they kept running after our approach and successfully departed the swamp and possibly all of Fire Country, and we just weren't able to find a trail, or
D) something we haven't even thought of
Without manually searching the swamp (and dealing with the exponential problems of search), we, the Konoha rangers, would have no idea which of those were true.
4) Consider the perspective of Mist decision-makers who ordered our deaths. If we were playing them, what would our objectives for this operation have been? Terminate a large number of problem shinobi in one fell swoop, with minimal loss of resources. Assuming we are extremely lucky and get info from a shinobi who survived the fight and ran back to Mist, we know the site of the battle and can send trackers there to look. Reluctantly, we send Zabuza, despite the massive opportunity costs incurred by having him perform non-revenue-generating work. If we do not endow Zabuza with the authority to risk an international incident by crossing into whatever countries he wants, he comes back to us and asks for permission to enter Fire Country. We then have to decide whether this is worth risking an international incident.
As a risk-averse human, we must consider the worst case scenario: somehow this spirals out of control WWI-style and we enter a Shinobi World War that destroys Mist, nay, the world. We must be appropriately pessimistic.
We may then consider the unlikely, but possible bad-case scenarios: Zabuza runs afoul of a particularly strong Leaf patrol and dies. Senju Tsunade runs into Zabuza and obliterates him, whether intentionally or during one of her drunken rampages. Zabuza does something impulsive in the heat of the moment and causes an international incident that will cost us standing and face.
We may then consider the somewhat likely bad-case scenarios: Zabuza finds the targets, but is killed by their multiple jounin. Or Zabuza isn't killed, but is wounded and must retreat, dying in Leaf territory. Or, even worse, Zabuza isn't killed, but is wounded and subsequently captured in Leaf territory. Zabuza searches Fire Country without being detected, but fails to find a trail, wasting all the time, costs, and risks of sending him. Or he finds a trail, but at some point the trail is broken and goes cold. Or he is intercepted by a Leaf patrol and survives, but must retreat (wasting all the time, costs, etc).
There are also the good-case scenarios, but if those happen we just get the benefits (discussed below) with minimal costs.
If we send more people with Zabuza: the fixed costs increase. The risk of international incident and catastrophic war increases, albeit minorly. The risk of Konoha detection increases, as not every jounin is likely to be as competent as Zabuza. Our losses if they run into Senju Tsunade increase. However, our expected losses if they find the targets and engage them decrease. Is that worth the other risks? Hard to say.
So, the expected cost equals -
[Large fixed cost of Z not generating revenue] + [Very small risk (<1%) of catastrophic loss] + [Pretty small (<5%) risk of terrible loss] + [Difficult to calculate [~10-40%] risk of loss]
Optional: [Additional large fixed cost of sending more jounins on a non-revenue generating mission] + [Marginal increase in risks of catastrophic and terrible loss]
We could mitigate the risks originating from Leaf forces by going hat-in-hand to Sarutobi and begging him, but do we really want to owe a favor to the God of Shinobi? Asking to deploy a kill team with license to engage in (extremely collateral-damage-prone) jounin-level combat is not exactly a small favor either.
If we DID endow Zabuza with the authority to enter any country and risk an international incident for this mission beforehand, we would still have had to make this calculus beforehand.
If we DIDN'T receive info from a surviving shinobi, our decision-making is delayed by the several days/weeks it takes to get suspicious, send a guy there, and have him return with his forensic report of what the hell happened, but is otherwise essentially the same. Unless he fails to find the battle site, in which case we're shit out of luck.
Now let's consider our expected gains from finishing off this band of problem shinobi. Our objective was to have them killed with no muss and no fuss. Well, that's already out the window. However, we do know the majority of these jounins killed each other during the internecine engagement, which means our objective is already partially complete. So, what can we expect to gain from this mission, if we are lucky enough for everything to go off without a hitch?
A) We kill off those shinobi that were not already killed in the internecine strife. A mediocre benefit, since that same strife already ensured that the group was too weak to challenge us.
Any other benefits? We don't get the standard benefits for hunting down missing-nin, enforcing the reputation of Hidden Mist and deterring defectors, because of our cover story. Ostensibly these were loyal shinobi sent on a tactically ill-advised mission that ended up killing them. In order to declare them missing-nin, we would first have to declare them traitors, which raises all sorts of questions. To address those questions we would have to come up with an even more contrived story, and no story that contrived is airtight enough to escape the suspicion of competent jounin. People will wonder why their friends and family members were involved in this bizarre string of events, and begin digging. People will be motivated to "prove" that their friends aren't actually traitors, which is quite possibly because many weren't actually traitors. Oh the tangled webs we weave, when we try to dispose of subordinates without a fight! I knew we should have just had them assassinated.
Anything else? The continued existence of these missing-nin could be a problem, if it were revealed they originated from Mist. But missing-nin have no incentive to advertise the fact that they're missing-nin, and most have strong incentives to pretend not to be ninja at all. The risk-mitigation benefits of even a successful hunt are very small, relative to that mission's cost. Their party is too small and weak to challenge us, and they have no reason to participate in conspicuous anti-Mist activities, since they will likely assume we're committing tons of resources to hunting them down. Hey, we can get most of the benefits of hunting them down without actually hunting them down, due to their own paranoia!
It's nice to tie up loose ends, but when the cost is this high we have to seriously ask ourselves whether it's worth it. Even if the mission is successful, that doesn't mean we'll avoid one of the terrible or catastrophic losses. Zabuza could successfully hunt them down, or successfully kill them all - and then die from wounds on the way back, or run into Tsunade on the way back, or be captured due to his wounds on the way back, just as easily - if not more easily - than on the way forward.
The calculus, then:
[Large fixed cost of Z not generating revenue] + [Very small risk (<1%) of catastrophic loss] + [Pretty small (<5%) risk of terrible loss] + [Difficult to calculate [~10-40%] risk of loss]
In exchange for -
[Killing off an already eviscerated group of shinobi unlikely to trouble us further]
While this may be an imperfect simulation of the Mist decision-makers, there would need to be absolutely MASSIVE unknown benefits or similarly massive cost-reducers for this to result in Zabuza's actual deployment. If these shinobi had critical artifacts we couldn't let fall into the wrong hands or something, that would be different, but they don't have anything like that because we sent them into battle as our means of killing them. We would have to have been holding the idiot ball to kill them this way if their capture could damage Mist; anything can happen in battle, after all.
The benefit is so meh that just the opportunity cost of Zabuza not generating revenue would probably deter me from wasting time on this. Label 'em MIA, one more casualty of the fog of war, and be glad this didn't cost more than it already has. We've got five hundred other problems to attend to in the course of running a ninja village.
Bonus - Other Considerations
5) What if Shikigami-sensei killed the legitimate authority and forged those papers?
I think this is improbable for three reasons.
A) First, Hidden Villages have a very strong incentive to produce validation methods that even civilians can recognize, but even jounin can't fake, for a huge number of reasons. If your contracts, agreements, and orders don't have ironclad validation, your entire infrastructure falls apart. This is doubly so in a world where the main conflicts are resolved by ninjas.
B) Second, mass movements involving twelve+ jounin and huge numbers of lesser nin (our initial party) into international territory are extremely unusual for peacetime Hidden Villages to make. What possible legitimate objectives, short of outright conquering a minor village, would justify that number of jounin deployed?
C) Third, Shikigami admitted that his plan was very risky. The only reason to intentionally strand us in straits this dire is if he thought the chance of his own death upon staying loyal was close to 100% - and if that were the case, the Mizukage would just have killed him rather than allowing him to be sent on a mission.
However, if he did indeed do those things, then the situation is A LOT better for us.
First, the difficulty of sedition scales nonlinearly with the number of required conspirators, so the Mizukage is likely to conclude that it was caused by one or a few jounin. Second, the expected benefits of finding us go from "pretty much nothing" to "successful recovery of several jounin and bloodline users." Third, as mere genin, we are the least likely to be blamed for Shikigami's shenanigans. Killing an academy-validated genin means wasting all the budget and time spent raising them, so it's worth it to keep us alive. Fourth, in order to credibly approach us without our fearing a trick, the Mizukage would have to immediately place us in a situation where he could trivially kill us, but does not. That means overwhelming force + S-rank ninjas, which means he'll have to ask Sarutobi for a huge favor - but if the benefits are relevant, then that favor stings a lot less.
6) Given the cost-benefit analysis of the Mizukage's actions, it seems the easiest and cheapest route for him is just to tell Sarutobi about us.
This is true, to an extent. However, even that path is not without cost.
If the Mizukage says we're missing-nin to be hunted down, he will be admitting to the God of Shinobi that Mist just lost over twenty-five (!) ninja. That is an extremely terrible admission to make, for obvious reasons. Sudden losses of that magnitude don't happen without something shady, in policy or infrastructure. What if Leaf scents weakness? What if Sarutobi's "peaceful" facade was merely, as they've always suspected, a ploy?
If he paints us as especially dangerous and powerful, then he's admitting that Mist just lost the services of twenty-five especially dangerous and powerful ninja!
If the Mizukage wants Sarutobi to do his dirty work, he needs to inform Sarutobi about the nature of that work and the units involved, which is made even more awkward by the cover story. If he tells the Hokage that we're missing-nin but keeps to the cover story with Mizugakure, then he basically hands the Hokage a social Sword of Damocles. If he tells the Hokage that we're loyal nin that need to be extracted, that's basically begging Konoha for help and will instantly be discredited when the Hokage's subordinates tell him what we tell them. And he knows this.
And all of that's not even getting into the difficulty of putting one over the God of Shinobi.
But the most pressing issue is this: there is no reason for the Mizukage to even risk this interaction, because even if the costs are "lower," the benefits are still nearly nonexistent. That said, this scenario is a possibility and we should plan for it, in fact we should assign a higher probability to it than the chance they actually send a full hunter team this deep into Fire (which we should also still plan for, despite it being unlikely - we just shouldn't allow it to dominate our every move). But refer again to the section on the Konoha rangers: if even the people following us have no way of knowing whether we're in the swamp or just passing through, then some dudes five hundred miles away in their Kage towers, reading info filtered through three levels of sub-reporting, will have even less idea.
Sarutobi may care, in principle, that some badly-harried dudes might be hanging out somewhere in the Swamp of Death. But is he willing to risk the lives of 4+ jounin to search that hellhole when the Mist-nin could just as easily have been passing through? Now, if they do make trouble, then the costs are clarified and the incentives change. But if they're not doing anything - if he can't even confirm, without extensive resource expenditure, that they're even there - well, those 4+ jounin could be out earning money for the village on less risky affairs. That money means orphanages and hospitals and kunai and schools. It means civilians fed that would otherwise starve, roads maintained and palms greased, less of the jounin council breathing down his neck.
The lesson of cost-benefit analysis is that principles cost resources to maintain. Only the all-powerful can infallibly enforce his principles no matter where the transgression occurs. And while a Kage may be powerful, he is not all-powerful. Likely he has problems far more pressing than this.
7) We are not the only ones operating from a position of scarce resources.
We are not the only ones ignorant of our enemy's intentions, motives, and current plans.
We are not the only ones on whom "a rational world" imposes limits of practicality, imperfect information, and economic feasibility.
We are not alone.
Marked for Death Quest: It Could Be Worse.
*GMs, if any of the assumptions I've made are invalid in a way that our character or people he'd ask (his sensei, mostly) would know or suspect, please do speak up!
