Hey thats a really great Idea! New Games are always fun. Here are a few of my suggestions off the bat:
Modulation Games: What about modulation in key? I rarely ever know how to do that successfully - and I've always wanted to see it done well before my very eyes. So maybe we could have melodies, that people could modulate into different keys?
Question and Answer: Another Game which I haven't played for years is "Question and Answer". Thats basically where someone improves something on say a piano, and the other person tries to respond to that phrase with something that either continues the 'story' or the logical unravelling of the melody or the abstract phraseology/algebra of the music in inventive and often quite amusing ways. This would require purely melody only. But instead of say, harmonizing a melody - someone could post a short phrase - which requires someone to respond to it. All using the same instrument. And it could be altered numerous times. And each time someone added to it, you could decide which version you liked more. Each person could have 4 bars for example, or even simply 2 bars. And then, you could take the piece you enjoyed and write your own reply. Forming endless musical 'conversations'. Until you decided you were done with that piece! It would be great inspiration for composing - you wouldn't need to invent your own melodies so much as participate in the melodies of others - even steal/borrow from ideas of other composers to create your own music! With due deferrence of course
Then when we have finished with the melody - someone can harmonize it! Just a suggestion
Multiple Question and Answer: Alternatively you could say have a quartet, involving question and answer again (which is a basic compositional technique I suppose now that I come to think of it) and each person could take the role of one instrument. So one person could be the first violin, the other the 2nd violin, viola, cello, etc. This would allow someone to write out a full melody, employ some kind of counterpoint, and then harmonizing, etc. It would vary wildly - there would have to be distinct rules....still - I don't know.
Fugual Games: What about Fugues? Fugues and Counterpoint are always great ways of experimenting with melodies and harmonizes. I suppose thats already available in the current format. You could have 'form specific' games as !Mark! suggested - like having particular ensembles. Or even music from particular styles, eras.
Imitation Games: You could have imitation games - like take a certain famous nocturne of Chopin and write on in a similar key, if not the same key - in imitation of it. Like, trying to capture the same feeling, etc.
Theme/Inspiration Games You could have say, a poem, or a picture, or some description, or prescribe a novel to read (pretty instensive though) and then have people reflect and discuss upon it - and then they are given a set period to compose a piece that would be the equivalent of a tone poem, or a sonata, or something of that kind - to demonstrate how they interpreted the piece/reacted to it/how it affected them. If necessary I will gather random poems - as that kind of creative cross-fertilization is one of my hobbies!
Well, I ran out of creative juice - they were just a few ideas. Tell me what you think! Ciao for now,
Pravin