# Proofs of security for anonymity in a multi-party setting

I'm looking for material that proves the anonymity of parties in a non-interactive setting. I would like to know if there are simulation based proofs (UC) and property based proofs (game based) for anonymity that I can look at.

Also when when proving such a protocol to be anonymous, how is one supposed to define anonymity? My main confusion I guess is how does one define the security of a system that shows anonymity, i.e. the system does achieve anonymity.