ABSTRACT
In this chapter, we do not intend to make an exhaustive review of everything what the Shapley value has meant in the scientific literature, but simply to show a few brushstrokes that serve as an initial and introductory chapter for this book dedicated to the Shapley value. We will first present some of its very well-known mathematical expressions, starting with those introduced by Lloyd Shapley in 1953. Secondly, we present some of its most important characterizations as indication of the large number of appealing and interesting properties that this value satisfies. Finally, we select a sample of the Shapley value extensions to a large number of contexts and their applications to very different fields and sceneries. All this in order to show that the Shapley value is highly valued by many researchers as an useful and relevant model to analyze, both from a theoretical and applied perspective, allocation problems in the most general sense.
