Abstract
In 1953, Shapley proposed a solution concept for cooperative games with transferable utility. The Shapley value is a unique function which obeys three axioms — symmetry, efficiency and additivity. The aim of our article is to provide a new axiomatic approach which classifies the existing values (indices). Shapley’s efficiency and symmetry conditions are kept whereas the additivity axiom is replaced by the axiom of global monotonicity. The Shapley value satisfies the new set of axioms. Some other values (indices) also satisfy the new set of axioms. However, our extension of the set of acceptable values (indices) excludes the Banzhaf-Coleman and Holler-Packel indices.
This research was undertaken with support from the European Commission’s ACE Phare Programme 1994, project No. 94-0666-R, and cosponsored by the Grant Agency of the Czech Republic, project No. 402-96-1049. We are grateful to František Turnovec and Elena Mielcová from CERGE-EI, Manfred J. Holler from the University of Hamburg and Hugh Ward from the University of Essex for their interest and helpful suggestions.
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Levínský, R., Silárszky, P. (2001). Global Monotonicity of Values of Cooperative Games: An Argument Supporting the Explanatory Power of Shapley’s Approach. In: Holler, M.J., Owen, G. (eds) Power Indices and Coalition Formation. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-6221-1_7
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DOI: https://doi.org/10.1007/978-1-4757-6221-1_7
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