The Shapley Value of Tuples in Query Answering

Authors Ester Livshits, Leopoldo Bertossi, Benny Kimelfeld, Moshe Sebag

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Ester Livshits
  • Technion, Haifa, Israel
Leopoldo Bertossi
  • Univ. Adolfo Ibañez, Santiago, Chile
  • RelationalAI Inc., Toronto, Canada
Benny Kimelfeld
  • Technion, Haifa, Israel
Moshe Sebag
  • Technion, Haifa, Israel

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Ester Livshits, Leopoldo Bertossi, Benny Kimelfeld, and Moshe Sebag. The Shapley Value of Tuples in Query Answering. In 23rd International Conference on Database Theory (ICDT 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 155, pp. 20:1-20:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


We investigate the application of the Shapley value to quantifying 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. We study this measure in the context of conjunctive and aggregate queries by defining corresponding coalition games. We provide algorithmic and complexity-theoretic results on the computation of Shapley-based contributions to query answers; and for the hard cases we present approximation algorithms.

Subject Classification

ACM Subject Classification
  • Theory of computation → Data provenance
  • Shapley value
  • query answering
  • conjunctive queries
  • aggregate queries


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