Like when someone asks for an egg will it just be the first breeder who is able to get it?
The breeder refers to us?
I think you misinterpreted something.

What I meant/was trying to say:
We make a list for each day of the week as to which Pokémon goes up for trade for a random catchable Pokémon in the wild. Then, the first person to the GTS and trades it, wins/receives it. We could do multiple ones per day, it depends on the availability.
Or we could:
A completely random Daily-Trade.
We breed Pokémon and we put up a trade on the GTS when we have a Pokémon ready or something. (I don't have a clear imagine in my mind of this.)
Always open for more suggestions.