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The rule Shared Power states:
"If your warlord is chosen from this formation, all of the models in the Infernal Tetrard also have the model's warlord trait...etc".

The problem is that all the warlord traits specifically state that they affect the warlord. And those other daemon princes don't become the warlords.

According to the faq you treat the other princes as warlord for the warlord trait

There's nothing in the 1.2 faq

It is in the 'Curse of the Wulfen' FAQ, not the 'Daemon' FAQ:

"Q: Does Shared Power from the Infernal Tetrad treat each
Daemon Prince as if it were the Warlord, or do Warlord Traits
with wordings like ‘your Warlord receives X’ only affect the
actual Warlord? Do these effects stack?
A: When using Shared Power, the other models in the
Infernal Tetrad have the same Warlord Trait that you
generate for your Warlord. This affects each of the
Daemon Princes as if they were your Warlord, and they
each benefit individually from the rule. For example,
if you generated the Savage Hedonist Warlord Trait,
you would add 1 to the Attacks characteristic of each
of the models, not 4 to the Attacks characteristic of
your Warlord. The effects are never cumulative – a unit
within 7" of two or more models with the Miasma of
Pestilence Warlord Trait would only suffer D6 additional
Strength 1 hits with the Poisoned special rule at the end
of the phase, not 2D6 or more. For another example,
if the models in the Infernal Tetrad have the Strategic
Genius Warlord Trait, you would only add 1 to your roll
to Seize the Initiative, not 4."