### A Note on Construction of a Composite Index by Optimization of Shapley Value Shares of the Constituent Variables

#### Abstract

**Abstract. **This paper proposes a method to construct composite index, which is a linear combination of several variables, by deriving weights on the criterion of Shapley value (from cooperative game theory) that a constituent variable has in making the composite index. In practice it is found oftentimes that the most common method of principal component analysis has a tendency to ignore (or poorly weigh) those constituent variables that do not have strong correlation with the sister variables. This elitist nature of PCA forces a compromise upon the analyst’s desire and need to incorporate those weakly correlated (but theoretically and practically important) variables into the composite index. In that case, one must construct a composite index that is more inclusive in nature. The Shapley value based composite index meets that requirement.

**Keywords.** Shapley value, Composite index, Principal Component Analysis, Inclusive indices, Global optimization.

**JEL.** C43, C63, C71.

#### Keywords

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DOI: http://dx.doi.org/10.1453/ter.v3i3.903

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