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：暂无翻译