> Logically, the first two civilizations to "team up" would easily handle any single civilization that challenges them.

I don't think saying "logically" and then an unsubstantiated claim constitutes a proof.

If two civilizations team up, whether that makes them stronger, weaker, or equally effective, is not certain IMO.

When two human companies merge, the result is often mistrust, poor communication, poor effectiveness, and sometimes ultimately failure. Sometimes the result of the merger is more effective.

A single, decisive government can run more effective than an indecisive coalition with no clear leader.

I just don't see how a definitive conclusion is possible any way. Surely it would vary case by case.

>When two human companies merge, the result is often mistrust, poor communication, poor effectiveness, and sometimes ultimately failure. Sometimes the result of the merger is more effective.

Those are all important considerations when talking about particular circumstances. Mathematically, however, 2 is greater than 1.

I say "logically" in the sense that, across a broad view of conflicts, the larger combatant usually does the most damage. The reason why is particular to each conflict (more bodies to throw, more brains devoted to tech development, more industrial output, etc.), and when it does not happen, the reason why is also similarly particular. You can also argue whether the circumstances truly yield a "win" (as in asymmetric warfare that ends with the smaller force driving out the larger one on logistical grounds, despite sustaining heavier losses). (Also note that "war" is not "business"; alliances are more important when the outcome of lost battles isn't just lost access to capital, but lost lives).

To go from 1 to 2, is possible by alliance or by subjugation.

> Logically, the first two civilizations to "team up" would easily handle any single civilization that challenges them.

This assumes defense is possible. Two loud cooperating civilizations don’t seem like they’d stand much of a chance against a silent, hostile civilization that quietly chucks a few rocks at both homeworlds and any interesting-looking moons, timed to arrive at roughly the same time.

A silent, hostile civilization that applies the astronomical levels of energy to accelerate enough mass to cause an extinction level event at the target in any reasonable amount of time would very likely cease to be a silent civilization. It imagine it would be difficult to hide an energy expenditure of that magnitude; the target may even be capable of deflecting the incoming relativistic payload with one of their own given enough lead time. Also, if there are sufficient loud, cooperating civilizations paying attention to large bursts of energy in their neighborhood, the asshole rock-chucking civilization may find multiple such relativistic payloads heading for their home relatively soon after firing theirs.

Send an agent to an uninhabited star system and launch the rocks from there. Everyone that can see would see the energy expenditures, but they would get very little information other than the knowledge that a stealth based hostile civilization exists. This information would encourage everyone else to be less noisy.

The "stealthy" civilization has ceased to be stealthy, in this case. Launching an attack of any kind defeats the purpose, if anyone but the fully-wiped-out target can see. Your example suggests that a stealthy, hostile civilization isn't possible.

What would an observer see? It’s plausible that they would see an attack from an uninhabited solar system but not be able to find the home location of the attacker.

Ooh, that's the fun part. What (augmented) sense does the observer rely on? On what timescale? How was the attack coordinated? The attack surface of the operation - and the ability to trace it back to its origin - might be wider than you can plan for. "Plausible" is a shaky ground to be on with your civilization in the balance, if you suspect there's even a chance you can be discovered and have chosen to remain as hidden as possible heretofore. Dark Forest doctrine and hostility are incompatible, I think.