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Two different forms of responsibility, counterfactual and seeing-to-it, have been extensively discussed in philosophy and AI in the context of a single agent or multiple agents acting simultaneously. Although the generalisation of counterfactual responsibility to a setting where multiple agents act in some order is relatively straightforward, the same cannot be said about seeing-to-it responsibility. Two versions of seeing-to-it modality applicable to such settings have been proposed in the literature. Neither of them perfectly captures the intuition of responsibility. The paper proposes a definition of seeing-to-it responsibility for such settings that amalgamate the two modalities. The paper shows that the newly proposed notion of responsibility and counterfactual responsibility are not definable through each other and studies the responsibility gap for these two forms of responsibility. It shows that although these two forms of responsibility are not enough to ascribe responsibility in each possible situation, this gap does not exist if higher-order responsibility is taken into account.