An optimistic fair exchange (OFE) protocol is an effective tool helping two parties exchange their digital items in an equitable way with assistance of a trusted third party, called arbitrator, who is only required if needed. In previous studies, fair exchange is usually carried out between individual parties. When fair exchange is carried our between two members from distinct groups, anonymity of the signer in a group could be necessary for achieving better privacy. In this paper, we consider optimistic fair exchange of ring signatures (OFERS), i.e. two members from two different groups can exchange their ring signatures in a fair way with ambiguous signers. Each user in these groups has its own public-private key pair and is able to sign a message on behalf of its own group anonymously. We first define the security model of OFFERS in the multi-user setting under adaptive chosen message, chosen-key and chosen public-key attacks. Then, based on verifiable encrypted ring signatures (VERS) we construct a concrete scheme by combining the technologies of ring signatures, public-key encryption and proof of knowledge. Finally, we show that our OFERS solution is provably secure in our security model, and preserving signer-ambiguity of ring signatures. To the best of our knowledge, this is the first (formal) work on this topic.