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Dynamic resource allocation in fuzzy coalitions: a game theoretic model

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Abstract

We introduce an efficient and dynamic resource allocation mechanism within the framework of a cooperative game with fuzzy coalitions (cooperative fuzzy game). A fuzzy coalition in a resource allocation problem can be so defined that membership grades of the players in it are proportional to the fractions of their total resources. We call any distribution of the resources possessed by the players, among a prescribed number of coalitions, a fuzzy coalition structure and every membership grade (equivalently fraction of the total resources), a resource investment. It is shown that this resource investment is influenced by the satisfaction of the players in regard to better performance under a cooperative setup. Our model is based on the real life situations, where possibly one or more players compromise on their resource investments in order to help forming coalitions.

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Notes

  1. Interested reader may look at Borkotokey and Neog (2010), where we have developed a model to show how satisfaction of players can be incorporated in payoff allocation.

  2. The coalition structure \(\mathbf{S}^{Q}(m,n)\) can be thought of as a bundle of \(m\) distinct boxes such that each box has some maximum capacity to be determined by the amount of available resources.

  3. It was indeed intuitive to take a linear function that can approximate the actual satisfaction function in our problem. Nevertheless, more complex forms of the approximate function (of higher order) can possibly provide a better approximation in less time. Since this idea leads to a complete different model setup so we keep it for a future work.

  4. This may be the case when the three players decide to invest only on the first two venturs as the third one is found to be less profitable.

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Acknowledgments

The authors gratefully thank the Associate Editor, the Managing Editor and the three anonymous reviewers for the improvement of the paper. The suggestions of the Editor-in-chief are also greatly acknowledged.

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Authors and Affiliations

  1. Department of Mathematics, Dibrugarh University, Dibrugarh, 786004, India

    Surajit Borkotokey & Rupok Neog

Authors
  1. Surajit Borkotokey
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  2. Rupok Neog
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Correspondence to Surajit Borkotokey.

Additional information

This work was partially supported by grants MRP, UGC-India 42-26/2013(SR).

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Borkotokey, S., Neog, R. Dynamic resource allocation in fuzzy coalitions: a game theoretic model. Fuzzy Optim Decis Making 13, 211–230 (2014). https://doi.org/10.1007/s10700-013-9172-y

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