The Shapley Value in the Non Differentiable Case.

Abstract

In their book Values of Non Atomic Games, Aumann and Shapley (1974) define the Shapley value for non atomic games, and prove existence and uniqueness of it for a number of important spaces of games like pNA and bv'NA. They also show that this value obeys the so-called diagonal formula, expressing the value of each infinitesimal player as his marginal contribution to the coalition of all players preceding him in a random ordering of the players. The basic definitions are given in Section 1 of this document. Section 2 defines the probability distribution over perturbations and shows its uniqueness. An explicit formula for the value of games of the type discussed above (n-handed glove markets, majority in several different houses) is derived in Section 3.

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Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1983
Accession Number
ADA136471

Entities

People

  • J. F. Mertens

Organizations

  • Stanford University

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DTIC Thesaurus Topics

  • Algebra
  • Boolean Algebra
  • Computations
  • Continuity
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  • Equations
  • Estimators
  • Game Theory
  • Operations Research
  • Probability
  • Probability Distributions
  • Random Variables
  • Social Sciences
  • Statistical Algorithms
  • Step Functions
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  • Topology

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