The Iron Throne and Compelled by the King let me win dominance, no matter if I have standing characters or not.

What about winning a challenge with cards like Misinformation? I think the rule "must have STR > 0 and at least 1 character still stands, right?

Also, what happens when both players play misinformation (in this case I suspect the player who played it second wins).

For the iron throne you don't need anything to be standing or gold in order to win.

For the automatically win events, you still need to

a) Declare at least an attacker - otherwise you are not considered to have initiated the challenge.

b) Even if you have 0 strength at the time of the challenge resolution but your opponent has declared a defender, if you play the event you will win.

c) If you have 0 strength at the challenge resolution and your opponent's defending strength is also 0, then you cannot play the event. That is because your opponent won't win the challenge in this case, and neither will you. And Misinformation specifies "if an opponent would win an Int challenge against you, cancel"

d) You can play the event when you're the defender even if you don't have any defenders declared.

Rogue30 said:

To kind of clarify all the different scenarios Zsa put forth: No, the "must have STR > 0 and at least 1 participating character to win the challenge" does NOT stand when you play Misinformation or Feigned Retreat. This is because those restrictions are checked before the "cancel determination of challenge winner" events are played. Automatically winning the challenge bypasses those restrictions.

If I use one of those automaticall win events in defense and no defenders, I cannot use The Tower of Joy, right? I mean 0 is always fewer participating characters, but "participating" is a requirement here, correct?

Rogue30 said:

You can use it.

"I won the challenge. How many participating characters did I have?"

"0."

"How many did you have?"

"1."

"0 is less than 1. I have fewer participating characters, so the play restriction is met."

The requirements here are "winning" and "fewer."