Polluted river problems and games with a permission structure

René van den Brink, Simin He, Jia Ping Huang*

*Corresponding author for this work

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When a polluted river passes through several different regions, a challenging question is how should the costs for cleaning the river be shared among the regions. Following Ni and Wang (2007) and Dong et al. (2012), we first show that the Upstream Equal Sharing method and the Downstream Equal Sharing method coincide with the conjunctive permission value (van den Brink and Gilles, 1996) of an associated game with a permission structure, which is obtained as the Shapley value of an associated restricted game. Two main advantages of this approach are (i) we obtain new axiomatizations of the two sharing methods based on axiomatizations of the conjunctive permission value, and (ii) by applying the alternative disjunctive permission value, obtained as the Shapley value of a different restricted game, we propose the new Upstream Limited Sharing method and provide an axiomatization.

Original languageEnglish
Pages (from-to)182-205
Number of pages24
JournalGames and Economic Behavior
Early online date18 Oct 2017
Publication statusPublished - Mar 2018


  • Axiomatization
  • Cost sharing
  • Permission values
  • Polluted river


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