AN EXPLICIT FORMULA OF THE SHAPLEY VALUE FOR THE CONJUGATE-POINT GAME

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Description

The conjugate point was introduced by Jacobi to derive a sufficient optimality condition for a variational problem. One of the authors defined the conjugate point for an extremal problem in R^n. The key of the conjugate point is a coalition of variables. Namely, when there exists a conjugate point for a stationary solution x ∊ R^n, the solution is improved by suitably changing some of the variables. This fact leads us to a cooperative game. One of the solution concepts for cooperative games is the Shapley value. It evaluates player's contribution in the cooperative game. However, its calculation is usually very hard. The purpose of this paper is to provide a cooperative game, which we call the conjugate-point game, whose Shapley value can be explicitly computed.

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Details 詳細情報について

  • CRID
    1390572174802554112
  • NII Article ID
    120006401430
  • NII Book ID
    AA10634475
  • DOI
    10.5109/1906487
  • ISSN
    2435743X
    0286522X
  • HANDLE
    2324/1906487
  • Text Lang
    en
  • Article Type
    journal article
  • Data Source
    • JaLC
    • IRDB
    • Crossref
    • CiNii Articles
    • OpenAIRE
  • Abstract License Flag
    Allowed

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