Indifferential Privacy: A New Paradigm and Its Applications to Optimal Matching in Dark Pool Auctions

Public exchanges like the New York Stock Exchange and NASDAQ act as auctioneers in a public double auction system, where buyers submit their highest bids and sellers offer their lowest asking prices, along with the number of shares (volume) they wish to trade. The auctioneer matches compatible orders and executes the trades when a match is found. However, auctioneers involved in high-volume exchanges, such as dark pools, may not always be reliable. They could exploit their position by engaging in practices like front-running or face significant conflicts of interest, i.e., ethical breaches that have frequently resulted in hefty fines and regulatory scrutiny within the financial industry. Previous solutions, based on the use of fully homomorphic encryption (Asharov et al., AAMAS 2020), encrypt orders ensuring that information is revealed only when a match occurs. However, this approach introduces significant computational overhead, making it impractical for high-frequency trading environments such as dark pools. In this work, we propose a new system based on differential privacy combined with lightweight encryption, offering an efficient and practical solution that mitigates the risks of an untrustworthy auctioneer. Specifically, we introduce a new concept called Indifferential Privacy, which can be of independent interest, where a user is indifferent to whether certain information is revealed after some special event, unlike standard differential privacy. For example, in an auction, it's reasonable to disclose the true volume of a trade once all of it has been matched. Moreover, our new concept of Indifferential Privacy allows for maximum matching, which is impossible with conventional differential privacy.