An efficient, fair and stable solution to the river sharing problem

Research output: Working paperScientific

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Abstract

We consider the problem of sharing water among agents located along a river. A vector of property rights specifies how much water each agent is entitled to. The key concept in this study is an allocation's distance-to-reference vector. At an allocation, the distance-to reference vector specifies, for each agent, the amount of money that needs to be subtracted from the bundle the agent receives in order for the agent to be indifferent between the reference vector and the allocation. First, we characterize a social ordering function, called the reference-welfare equivalent Lorenz ordering, which ranks an allocation over another if the distance-to-reference vector of the former is more equal than the distance-to-reference vector of the latter. Second, we show that maximizing the reference-welfare equivalent Lorenz ordering over the set of acceptable allocations (defined in the sense of the core) leads to a class of solutions that meet the three key objectives of international river management: efficiency, fairness, and stability. We show that this class contains new solutions as well as the downstream incremental solution of Ambec and Sprumont (2002). Finally, we present an application of our approach to the case of the Blue Nile River Basin, shared among Ethiopia, Sudan and Egypt.
Original languageEnglish
Number of pages30
Publication statusPublished - Feb 2019
Externally publishedYes

Fingerprint

Water
Sudan
Ethiopia
Fairness
Property rights
Incremental
River basin
Egypt

Keywords

  • River sharing problem
  • Water sharing agreements
  • Fair allocations

Cite this

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title = "An efficient, fair and stable solution to the river sharing problem",
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An efficient, fair and stable solution to the river sharing problem. / Öztürk, Emel.

2019.

Research output: Working paperScientific

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N2 - We consider the problem of sharing water among agents located along a river. A vector of property rights specifies how much water each agent is entitled to. The key concept in this study is an allocation's distance-to-reference vector. At an allocation, the distance-to reference vector specifies, for each agent, the amount of money that needs to be subtracted from the bundle the agent receives in order for the agent to be indifferent between the reference vector and the allocation. First, we characterize a social ordering function, called the reference-welfare equivalent Lorenz ordering, which ranks an allocation over another if the distance-to-reference vector of the former is more equal than the distance-to-reference vector of the latter. Second, we show that maximizing the reference-welfare equivalent Lorenz ordering over the set of acceptable allocations (defined in the sense of the core) leads to a class of solutions that meet the three key objectives of international river management: efficiency, fairness, and stability. We show that this class contains new solutions as well as the downstream incremental solution of Ambec and Sprumont (2002). Finally, we present an application of our approach to the case of the Blue Nile River Basin, shared among Ethiopia, Sudan and Egypt.

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