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This research aims to investigate the application of the Shapley value to quantify the contribution of a tuple to a query answer. The Shapley value is a widely known numerical measure in cooperative game theory and in many applications of game theory for assessing the contribution of a player to a coalition game. It has been established already in the 1950s, and is theoretically justified by being the very single wealth distribution measure that satisfies some natural axioms. While this value has been investigated in several areas, it received little attention in data management. The aforementioned qualities of the Shapley value make it a better measure than several measures which have been suggested to quantify the contribution of a tuple recently. Furthermore, it allows us to compute responsibility with aggregation queries. We study this measure in the context of conjunctive and aggregate queries by defining corresponding coalitional games. We establish a dichotomy in complexity for the class of Boolean conjunctive queries without self-joins. In addition, we provide an efficient algorithm to compute the Shapley value in the tractable cases; and for the hard cases we present approximation algorithm. In the practical aspect, we implement these algorithms to study them empirically and find strategies and techniques to optimize them towards a practical application on realistic data.