In practice, collusive bidders' rings in English auctions with a single object frequently distribute collusive gains among ring members via sequences of re-auctions called knockouts. The present paper introduces a model of sequences of knockouts under the situation in which each bidder has information on his evaluation and the order of the evaluations of all bidders for the object. The present paper examines the distributive function of sequences of knockouts from the viewpoint of cooperative game theory. Each sequence of knockouts yields an element of the core, two particular sequences yielding the Shapley value and the nucleolus respectively. The present paper highlights the sequence of knockouts yielding the nucleolus.