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Promotion of cooperation when benefits come in the future: A water transfer case

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  • Cabo, Francisco
  • Tidball, Mabel

Abstract

This paper presents a two-regime differential game, with a first period in which two countries cooperate in a joint investment project to construct a specific infrastructure. This period ends when the infrastructure is finished, which serves to increase each player's welfare in a subsequent non-cooperative game played by the two countries thereafter. We define an imputation distribution procedure (IDP) to share the investment costs during cooperation according to each player’ future benefits. We prove that the IDP is time consistent if at any time within the cooperative period each country's share on the surplus to go is equal to or converges towards the country's relative gains from the existence of the infrastructure (realized in the subsequent non-cooperative period). Furthermore, we obtain the instantaneous side-payment scheme which makes the IDP feasible. The mechanism is studied for a joint investment project to build a water canal to transfer water between a surplus and a deficit river basin.

Suggested Citation

  • Cabo, Francisco & Tidball, Mabel, 2017. "Promotion of cooperation when benefits come in the future: A water transfer case," Resource and Energy Economics, Elsevier, vol. 47(C), pages 56-71.
    • Handle: RePEc:eee:resene:v:47:y:2017:i:c:p:56-71
    DOI: 10.1016/j.reseneeco.2016.12.001
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    1. Ambec, Stefan & Ehlers, Lars, 2008. "Sharing a river among satiable agents," Games and Economic Behavior, Elsevier, vol. 64(1), pages 35-50, September.
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    7. Cabo, Francisco & Erdlenbruch, Katrin & Tidball, Mabel, 2014. "Dynamic management of water transfer between two interconnected river basins," Resource and Energy Economics, Elsevier, vol. 37(C), pages 17-38.
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    9. Enrique Ballestero, 2004. "Inter-Basin Water Transfer Public Agreements: A Decision Approach to Quantity and Price," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 18(1), pages 75-88, February.
    10. Jorgensen, Steffen & Zaccour, Georges, 2001. "Time consistent side payments in a dynamic game of downstream pollution," Journal of Economic Dynamics and Control, Elsevier, vol. 25(12), pages 1973-1987, December.
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    Cited by:

    1. Francisco Cabo & Mabel Tidball, 2022. "Cooperation in a Dynamic Setting with Asymmetric Environmental Valuation and Responsibility," Dynamic Games and Applications, Springer, vol. 12(3), pages 844-871, September.
    2. Zhisong Chen & Keith C.K. Cheung & Manyi Tan, 2019. "Inter-Basin Water Transfer Supply Chain Coordination with Ramsey Pricing," IJERPH, MDPI, vol. 16(19), pages 1-22, September.

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    More about this item

    Keywords

    Cooperative differential game; Non-cooperative differential game; Imputation distribution procedure; Instantaneous side-payment; Time-consistent solution;
    All these keywords.

    JEL classification:

    • F18 - International Economics - - Trade - - - Trade and Environment
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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