Theory and Implementation of Sensitivity Analyses Based on Their Algebraic Representation in the Graph Model
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Sensitivity analyses based on an algebraic representation in the graph model for conflict resolution (GMCR) are generalized for ascertaining the robustness of stability results by varying decision makers’ preference ranking. The ordinal preferences in GMCR are advantageous to carry out sensitivity analyses with respect to systematically identifying the influence of preference alterations upon the four basic stabilities consisting of Nash stability, general metarationality, symmetric metarationality and sequential stability. The proposed algebraic representation of the four basic stabilities is not only effective and convenient for computer implementation of sensitivity analysis, but also makes it easier to understand the meaning of the four stabilities when compared with the existing matrix representation. Further, these sensitivity analyses results are embedded into the latest version of the decision support system NUAAGMCR, which can be used to study real-world conflicts. To illustrate how these contributions to sensitivity analyses can be applied in practice and provide valuable strategic insights, they are used to investigate the civil war conflict in South Sudan.
KeywordsSensitivity analyses algebraic expression graph model ordinal preference conflict resolution
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The authors would like to express their appreciation to the anonymous reviewers and Editor for their constructive comments which improved the quality of the paper. The authors are grateful for the financial support supplied by the National Natural Science Foundation of China (71471087, 71071076 and 61673209), a Discovery Grant from the National Sciences and Engineering Research Council of Canada, and the Ministry of Education Humanities and Social Science Planning Foundation of China (18YJA630128).
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