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Collusion rings pose a significant threat to peer review. In these rings, reviewers who are also authors coordinate to manipulate paper assignments, often by strategically bidding on each other’s papers. A promising solution is to detect collusion through these manipulated bids, enabling conferences to take appropriate action. However, while methods exist for detecting other types of fraud, no research has yet shown that identifying collusion rings is feasible. In this work, we consider the question of whether it is feasible to detect collusion rings from the paper bidding. We conduct an empirical analysis of two realistic conference bidding datasets and evaluate existing algorithms for fraud detection in other applications. We find that collusion rings can achieve considerable success at manipulating the paper assignment while remaining hidden from detection: for example, in one dataset, undetected colluders are able to achieve assignment to up to 30% of the papers authored by other colluders. In addition, when 10 colluders bid on all of each other’s papers, no detection algorithm outputs a group of reviewers with more than 31% overlap with the true colluders. These results suggest that collusion cannot be effectively detected from the bidding using popular existing tools, demonstrating the need to develop more complex detection algorithms as well as those that leverage additional metadata (e.g., reviewer-paper text-similarity scores).