To my knowledge, if an opponent cannot pay 2 for Prison, none of his creatures could attack me even if one of them equips Bloodthirsty Blade or has similar effect on it.
So assuming my opponent has two mana open and initiates combat, he has creature A and creature B (goaded), can he pay for just A and claim that he runs out of mana, therefore cannot attack with B?
Assuming he has no other opponent or planeswalker to attack, yes, he can do that.
508.1d. The active player checks each creature they control to see whether it's affected by any requirements (effects that say a creature attacks if able, or that it attacks if some condition is met). If the number of requirements that are being obeyed is fewer than the maximum possible number of requirements that could be obeyed without disobeying any restrictions, the declaration of attackers is illegal. If a creature can't attack unless a player pays a cost, that player is not required to pay that cost, even if attacking with that creature would increase the number of requirements being obeyed. If a requirement that says a creature attacks if able during a certain turn refers to a turn with multiple combat phases, the creature attacks if able during each declare attackers step in that turn.
Now, if the goaded creature has anything else to attack than the player with Ghostly Prison, it must attack (including if the only option is the player who goaded the creature, since it's not able to attack anyone else). It must either attack the Prison player and be paid for, or attack someone else, or a planeswalker if there is no elligible player.
I'm a former judge (lapsed), who keeps up to date on rules and policy. Keep in mind that judges' answers aren't necessarily more valid than those of people who aren't judges; what matters is we can quote the rules to back up our answers. When in doubt, ask for such quotes.
Compare Ghostly Prison with War Tax. If creatures are affected by War Tax's ability and the appropriate player declines to pay the War Tax cost for a goaded creature (upon declaring attackers), that creature is not able to attack at all, so it doesn't attack any player or planeswalker (C.R. 508.1d, 701.37). See also this thread and this thread.
To my knowledge, if an opponent cannot pay 2 for Prison, none of his creatures could attack me even if one of them equips Bloodthirsty Blade or has similar effect on it.
So assuming my opponent has two mana open and initiates combat, he has creature A and creature B (goaded), can he pay for just A and claim that he runs out of mana, therefore cannot attack with B?
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StaffShu Yun, the Silent Tempest WUR Voltron Control
Temmet, Vizier of Naktamun WU Unblockable Mirror Trickery
Ra's al Ghul (Sidar Kondo) and Face-Down Ninjas
Brudiclad, Token Engineer
Vaevictis (VV2) the Dire Lantern
Rona, Disciple of Gix
Tiana the Auror
Hallar
Ulrich the Politician
Zur the Rebel
Scorpion, Locust, Scarab, Egyptian Gods
O-Kagachi, Mathas, Mairsil
"Non-Tribal" Tribal Generals, Eggs