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Game theoretic approach for fertilizer application: looking for the propensity to cooperate

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  • S. Schreider
  • P. Zeephongsekul
  • B. Abbasi
  • M. Fernandes

Abstract

This paper continues the research implemented in previous work of (Schreider et al. in Environ. Model. Assess. 15(4):223–238, 2010 ) where a game theoretic model for optimal fertilizer application in the Hopkins River catchment was formulated, implemented and solved for its optimal strategies. In that work, the authors considered farmers from this catchment as individual players whose objective is to maximize their objective functions which are constituted from two components: economic gain associated with the application of fertilizers which contain phosphorus to the soil and environmental harms associated with this application. The environmental losses are associated with the blue-green algae blooming of the coastal waterways due to phosphorus exported from upstream areas of the catchment. In the previous paper, all agents are considered as rational players and two types of equilibria were considered: fully non-cooperative Nash equilibrium and cooperative Pareto optimum solutions. Among the plethora of Pareto optima, the solution corresponding to the equally weighted individual objective functions were selected. In this paper, the cooperative game approach involving the formation of coalitions and modeling of characteristic value function will be applied and Shapley values for the players obtained. A significant contribution of this approach is the construction of a characteristic function which incorporates both the Nash and Pareto equilibria, showing that it is superadditive. It will be shown that this approach will allow each players to obtain payoffs which strictly dominate their payoffs obtained from their Nash equilibria. Copyright Springer Science+Business Media New York 2013

Suggested Citation

  • S. Schreider & P. Zeephongsekul & B. Abbasi & M. Fernandes, 2013. "Game theoretic approach for fertilizer application: looking for the propensity to cooperate," Annals of Operations Research, Springer, vol. 206(1), pages 385-400, July.
  • Handle: RePEc:spr:annopr:v:206:y:2013:i:1:p:385-400:10.1007/s10479-013-1381-9
    DOI: 10.1007/s10479-013-1381-9
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    References listed on IDEAS

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    1. Terry L. Roe, 1996. "Applications of Game Theory in Agricultural Economics: Discussion," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 78(3), pages 761-763.
    2. Filar, J.A. & Gaertner, P.S., 1997. "A regional allocation of world CO2 emission reductions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 43(3), pages 269-275.
    3. Xiaotie Deng & Christos H. Papadimitriou, 1994. "On the Complexity of Cooperative Solution Concepts," Mathematics of Operations Research, INFORMS, vol. 19(2), pages 257-266, May.
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    Cited by:

    1. Behnam Malakooti & Mohamed Komaki & Camelia Al-Najjar, 2021. "Basic Geometric Dispersion Theory of Decision Making Under Risk: Asymmetric Risk Relativity, New Predictions of Empirical Behaviors, and Risk Triad," Decision Analysis, INFORMS, vol. 18(1), pages 41-77, March.
    2. Rohit Malhorta, 2016. "Demystifying Optimal Welfare Weights Controversy From A Social Strategist Perspective," Journal of Social and Economic Statistics, Bucharest University of Economic Studies, vol. 5(2), pages 33-48, DECEMBER.

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