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Data Cost Games as an Application of 1‐Concavity in Cooperative Game Theory

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  • Dongshuang Hou
  • Theo Driessen

Abstract

The main goal is to reveal the 1‐concavity property for a subclass of cost games called data cost games. The motivation for the study of the 1‐concavity property is the appealing theoretical results for both the core and the nucleolus, in particular their geometrical characterization as well as their additivity property. The characteristic cost function of the original data cost game assigns to every coalition the additive cost of reproducing the data the coalition does not own. The underlying data and cost sharing situation is composed of three components, namely, the player set, the collection of data sets for individuals, and the additive cost function on the whole data set. The proof of 1‐concavity is direct, but robust to a suitable generalization of the characteristic cost function. As an adjunct, the 1‐concavity property is shown for the subclass of so‐called “bicycle” cost games, inclusive of the data cost games in which the individual data sets are nested in a decreasing order.

Suggested Citation

  • Dongshuang Hou & Theo Driessen, 2014. "Data Cost Games as an Application of 1‐Concavity in Cooperative Game Theory," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:249543
    DOI: 10.1155/2014/249543
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    References listed on IDEAS

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    1. Pierre Dehez & Daniela Tellone, 2013. "Data Games: Sharing Public Goods with Exclusion," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 15(4), pages 654-673, August.
    2. Pierre Dehez, 2013. "Cooperative provision of indivisible public goods," Theory and Decision, Springer, vol. 74(1), pages 13-29, January.
    3. SCHMEIDLER, David, 1969. "The nucleolus of a characteristic function game," LIDAM Reprints CORE 44, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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