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-았/었으면 좋겠다 is a very common way to express a wish or hope in Korean. It means something like:

• I hope ...
• It would be nice if ...
• I wish ...

So 연주했으면 좋겠다 means the speaker wants that action to happen.

This is one of the most common learner questions.

In Korean, -았/었으면 좋겠다 is the usual pattern for expressing a personal wish, even when the wish is about the present or future.

So although 했- looks like a past form, in this pattern it often does not mean the action already happened in the past. Instead, it makes the wish sound more hypothetical or softer.

• 연주했으면 좋겠다 = I hope they play / I wish they would play
• 연주하면 좋겠다 can sound more like it would be good if they play, and is often less natural for a direct personal wish in this kind of context.

So here, 연주했으면 좋겠다 is the more standard way to say the speaker hopes the band will perform an encore.

Usually, no.

Even though 했으면 contains a past-looking form, in -았/었으면 좋겠다 it often expresses a present or future wish, not a completed past event.

So this sentence normally means the speaker wants the band to play an encore now or later.

If you really wanted to express regret about the past, Korean would often use something else, such as a form like 좋았을 텐데.

It comes from the verb 연주하다.

Step by step:

• 연주하다 = to play / perform music
• 연주하였으면 = if played / if would play
• 연주했으면 = contracted form of 연주하였으면

So 했 here is just the shortened result of 하였.

This kind of contraction is very common in Korean:

• 공부하였어요 → 공부했어요
• 말하였어요 → 말했어요
• 연주하였으면 → 연주했으면

Both are possible, but they feel a little different.

• 밴드가 marks 밴드 as the subject of the hoped-for action.
• 밴드는 would mark 밴드 as the topic, often with a feeling of contrast or emphasis.

So:

• 밴드가 앙코르를 연주했으면 좋겠다.
  = I hope the band plays an encore.
  Neutral, straightforward.

• 밴드는 앙코르를 연주했으면 좋겠다.
  = As for the band, I hope they play an encore.
  This can sound more contrastive, like maybe you are comparing them with someone else.

In this sentence, 가 is the most neutral choice.

Because 앙코르 is the object of 연주하다.

• 밴드가 = the band (subject)
• 앙코르를 = an encore (object)
• 연주했으면 좋겠다 = I hope they perform/play

So 를 is just the normal object marker here.

Even though 앙코르 is a borrowed word, it still follows normal Korean grammar.

연주하다 means to play music or to perform music, especially with instruments or as a musical act.

In this sentence, it means the band is performing an encore piece.

Compared with English, 연주하다 is more specifically musical than a general verb like do. So it fits well with bands, orchestras, instrumental performance, and musical pieces.

A slightly different wording might use a more general expression, but 앙코르를 연주하다 clearly emphasizes the musical performance itself.

좋겠다 is in the plain style. It is often used for:

• casual speech
• written narration
• inner thoughts
• talking to friends, depending on tone

It is not the polite form.

Politer versions would be:

• 밴드가 앙코르를 연주했으면 좋겠어요.
• 밴드가 앙코르를 연주하면 좋겠어요.
  (possible, but the first is the more typical wish form)

So 좋겠다 sounds like a plain statement of the speaker’s hope.

It is omitted.

Korean very often leaves out subjects like I, you, or we when they are obvious from context. In a sentence with -으면 좋겠다, the speaker’s feeling is built into the expression, so you do not usually need to say 나는 or 제가.

So the sentence does not literally contain I, but the meaning naturally includes the speaker’s wish:

• (나는) 밴드가 앙코르를 연주했으면 좋겠다.

Usually, the version without 나는 sounds more natural unless you want emphasis.