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Maximal Decompositions of Cost Games into Specific and Joint Costs

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  • Moreaux, Michel
  • Truchon, Michel

Abstract

The problem in which some agents joint together to realize a set of projects and must decide how to share its cost may be seen as a cooperative cost game. In many instances, total cost may naturally be decomposed into joint costs and costs that are specific to individual agents. We show that the maximal amount that can be attributed directly to each agent while yielding a problem for the joint cost that remains a cost game, is given by the minimal incremental cost of adding this agent to any of the possible coalitions of other agents. Thus, for concave games, it is given by the incremental cost of adding the agent to all others. We also show that a concave game yields a reduced game that is itself concave. Le problème où plusieurs agents entreprennent en commun un ensemble de projets et doivent décider du partage du coût total peut être vu comme un jeu coopératif. Dans certains cas, le coût total peut naturellement être décomposé en coûts joints et coûts spécifiques aux agents. On montre que le montant maximal qui peut être attribué directement à chaque agent, tout en donnant un problème de partage de coût joint qui constitue encore un jeu de coût, est donné par le minimum des coûts incrémentaux de l'adjonction de l'agent aux coalitions possibles des autres agents.

Suggested Citation

  • Moreaux, Michel & Truchon, Michel, 2002. "Maximal Decompositions of Cost Games into Specific and Joint Costs," Cahiers de recherche 0205, Université Laval - Département d'économique.
  • Handle: RePEc:lvl:laeccr:0205
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    File URL: http://www.ecn.ulaval.ca/w3/recherche/cahiers/2002/0205.pdf
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    References listed on IDEAS

    as
    1. Nathalie de Marcellis-Warin & Erwann Michel-Kerjan, 2001. "The Public-Private Sector Risk-Sharing in the French Insurance "Cat. Nat. System"""," CIRANO Working Papers 2001s-60, CIRANO.
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    Keywords

    Cost game; Decomposition;

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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