# The Shapley Value of Tuples in Query Answering

## TL;DR

This paper explores using the Shapley value from cooperative game theory to measure the contribution of individual tuples to query answers in databases, providing algorithms and complexity analysis.

## Contribution

It introduces a novel application of the Shapley value to data management, defining coalition games for conjunctive and aggregate queries, with algorithms and approximations.

## Key findings

- Algorithmic solutions for computing Shapley contributions.
- Complexity results for different query types.
- Approximation algorithms for hard cases.

## Abstract

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.