Shapley value

In what follows, we will cover transferable utility cooperative games (players can share utility via side payments) and two solution concepts the core of the game and the Shapley value, and also biform games that have found several applications in SCM. Not covered are alternative concepts of value, e.g., nu-... 

Theorem 11. The Shapley value, Tri for player i in an N—person non-cooperative game with transferable utility is ... 

Because the Shapley value is unique, it has found numerous applications in economics and political sciences. So far, however, SCM applications are scarce except for discussion in Granot and Sosic (2001) we are not aware of any other papers employing the concept of the Shapley value. Although uniqueness of the Shapely value is a convenient feature, caution should surely be taken with Shapley value the Shapley value need not be in the core, hence, although the Shapely is appealing from the perspective of fairness, it may not be a reasonable prediction of the outcome of a game (i.e., because it is not in the core, there exists some subset of players that can deviate and improve their lots). 

Shapley et al. [125] computed the pX a of benzoic and o-, m-, and p-hydroxy benzoic acids in order to understand the higher ability of the o-hydroxy benzoate to complex to the cationic surfactant headgroups in micelles and adsorbed films. Although the values did not show good agreement with the experimental data, the calculations provided a clear explanation for the unusual behavior of the o-hydroxy benzoate. 

Shapley, L. 1953b. A value for n—person game. pp. 307-317 in Contributions to the Theory of Games, Volume II, H. W. Kuhn and A. W. Tucker, editors. Princeton University Press. 

This is known as the agents are substitutes condition (Shapley [65]). A subset of agents together have greater economic value than all of them separately. It is implied by submodularity of V(-). 

Quigley, J. Walls, L. (2007) Trading reliabihty targets within a supply chain using Shapley s values. Reliability Engineering and System Safety 92(10) 1448 1457. 

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