We consider multi-user commitment models that capture the problem of enabling multiple bidders to simultaneously submit auctions to verifiers while ensuring that i) verifiers do not obtain information on the auctions until bidders reveal them at a later stage; and, ii) bidders cannot change their auction once committed. Specifically, we assume that bidders and verifiers have access to a noiseless channel as well as a noisy multiple-access channel or broadcast channel, where inputs are controlled by the bidders and outputs are observed by verifiers. In the case of multiple bidders and a single verifier connected by a non-redundant multiple-access channel, we characterize the commitment capacity region when bidders are not colluding. When the bidders are colluding, we derive an achievable region and a tight converse for the sum rate. In both cases our proposed achievable commitment schemes are constructive. In the case of a single bidder and multiple verifiers connected by a non-redundant broadcast channel, in which verifiers could drop out of the network after auctions are committed, we also characterize the commitment capacity. Our results demonstrate how commitment schemes can benefit from multi-user protocols, and develop resilience when some verifiers may become unavailable.

翻译：我们考虑多用户承诺模型，该模型旨在解决使多个投标者能够同时向验证者提交拍卖信息，同时确保：i) 验证者在投标者后续揭示拍卖信息前无法获取相关信息；ii) 投标者一旦承诺便不能更改其拍卖信息。具体而言，我们假设投标者和验证者拥有一条无噪声信道以及一条噪声多址接入信道或广播信道，其中输入由投标者控制，输出由验证者观测。在多个投标者与单个验证者通过非冗余多址接入信道连接的情况下，我们刻画了投标者不共谋时的承诺容量域。当投标者共谋时，我们推导了和速率的可达域与紧致逆界。在这两种情况下，我们提出的可达承诺方案均具有构造性。在单个投标者与多个验证者通过非冗余广播信道连接的情况下（其中验证者可能在拍卖承诺后退出网络），我们也刻画了承诺容量。我们的结果表明承诺方案如何从多用户协议中获益，并在部分验证者可能不可用时增强鲁棒性。