Global Monotonicity of Values of Cooperative Games: An Argument Supporting the Explanatory Power of Shapley’s Approach

  • René Levínský
  • Peter Silárszky


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.


Cooperative Game Power Index Coalition Formation Simple Game Winning Coalition 
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Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • René Levínský
    • 1
  • Peter Silárszky
    • 2
  1. 1.Institut zur Erforschung der wirtschaftlichen EntwicklungAlbert-Ludwigs-UniversitätFreiburgGermany
  2. 2.Center for Economic Research and Graduate Education (CERCE)Charles UniversityPraha 1Czech Republic

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