This page contains an incomplete list of related work. In the future, it will be expanded to have more detailed comparisons.
Privacy Pass is a privacy-preserving authentication protocol developed by George Tankersley, Filippo Valsorda, Alex Davidson, Ian Goldberg, and Nick Sullivan. Privacy Pass allows users to request single-use "tokens" from a server and redeem them unlinkably from their issuance. For instance, a user can obtain a collection of single-use tokens by solving a CAPTCHA, and later present those tokens to access web resources. This page contains a description of the protocol and various attack vectors.
In comparison to Danake tokens, which store a balance that can be drawn down in multiple spend transactions of different amounts, Privacy Pass tokens can be redeemed only once for an indivisible unit value. However, Danake's flexibility comes at a cost, as Privacy Pass redemptions are more efficient for the server.
Erinn Atwater and Sarah Jamie Lewis of OpenPrivacy are developing [extensions] to Privacy Pass which allow tokens to be purchased anonymously using cryptocurrency (e.g., shielded Zcash). These tokens can then be unlinkably redeemed for anonymous servers. This is the same use-case and threat model as Danake (TODO: check), but with more efficient token redemption.
Brave has a design for using Privacy Pass for privacy-preserving ad confirmations (authors?). Because Privacy Pass tokens have unit value, they suggest using different (domain-separated) token issuers to correspond to each token value denomination.
BOLT is a "Layer 2" system which provides privacy-preserving off-chain payment channels with escrowed funds. Either counterparty can close the channel and obtain their funds net of whatever payments occurred. This is a more sophisticated threat model than Danake, where the service provider issues credit according to arbitrary policy and is trusted to redeem credit.
Hyphae was an unimplemented design by Henry de Valence and Isis Lovecruft for an anonymous reputation-based distribution network for Tor bridges. It contains precursor ideas to Danake, in particular an AMACS-based micropayment system, but without credential epochs, key rotation, the wallet/token distinction, or Bulletproofs.
Unlinkable Serial Transactions was a 1997 proposal by Paul Syverson, Stuart Stubblebine, and David Goldschlag for anonymous service payments. In USTs, clients sequentially present certificates to a service provider, and the server responds to each presentation with blinded issuance of a new certificate. Although the cryptographic mechanisms are different, this protocol structure is the one used by Danake and Hyphae.
The serial structure of presentation-issuance means that it is not possible to make multiple payments in parallel. Danake addresses this by means of token sub-credentials; a user can purchase multiple tokens and use distinct tokens in parallel, even though each token spend performs a serial presentation-issuance flow.
Signal's private group design uses AMACs, with some extensions to allow attributes which are ElGamal-encrypted group elements.