Coalition formation is an important capability for automated negotiation among self-interested agents. In order for coalitions to be stable, a key question that must be answered is how the gains from cooperation are to be distributed. Coalitional game theory provides a number of solution concepts for this. However, recent research has revealed that these traditional solution concepts are vulnerable to various manipulations in open anonymous environments such as the Internet. To address this, previous work has developed a solution concept called the anonymity-proof core, which is robust against such manipulations. That work also developed a method for compactly representing the anonymity-proof core. However, the required computational and representational costs are still huge. In this paper, we develop a new solution concept which we call the anonymity-proof Shapley value. We show that the anonymity-proof Shapley value is characterized by certain simple axiomatic conditions, always exists, and is uniquely determined. The computational and representational costs of the anonymity-proof Shapley value are drastically smaller than those of existing anonymity-proof solution concepts.