Polluted River Problems and Games with a Permission Structure

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• 研討會日期 : 2014-09-23
• 時間 : 14:30
• 主講人 : Professor René van den Brink
• 主持人 : Professor Chun-Hsien Yeh
• 地點 : Conference Room B110
• 演講者簡介 : Professor Brink received his Ph.D. in Economics from Tilburg University in 1994. He is currently Professor of Economics at VU University Amsterdam. His research fields are Cooperative Game Theory, Game Theory, Microeconomic Theory, Networks, and Operations Research.
• 演講摘要 : A situation in which players in a cooperative transferable utility game (TU-game) are part of a hierarchical structure can be modeled by a game with a permission structure as in Gilles, Owen and van den Brink (1992). Dong, Ni and Wang (2012) consider cost sharing problems on a river network, shortly called polluted river problem, on rivers with multiple springs (sink tree structures) which generalizes the polluted river problem of Ni and Wang (2007) who only consider rivers with one spring. They introduce and axiomatize three cost sharing methods: the Local Responsibility Sharing (LRS) method, the Upstream Equal Sharing (UES) method and the Downstream Equal Sharing (DES) method. In this paper we model polluted river problems as games with a permission structure, where the permission structure is determined by the river structure. We show that the UES method can be obtained as the conjunctive permission value of the associated game with permission structure where the arcs (river segments) are oriented from upstream to downstream, and the DES method can be obtained by orienting the arcs in the reverse direction. We show that the axiomatization of the conjunctive permission value given in van den Brink and Gilles (1996) also yields uniqueness on the class of polluted river games and interpret these axioms in terms of water allocation principles from international water law. Moreover, looking at polluted river problems as games with a permission structure we can also apply the disjunctive permission value to obtain a new cost allocation rule where uncertainty about the upstream branch where pollution comes from yields lower contributions in the cleaning costs of certain upstream agents. We also show that the axiomatization of the disjunctive permission value in van den Brink (1997) yields uniqueness for polluted river problems and interpret the axioms in terms of water allocation principles.