Theory and Implementation of Sensitivity Analyses Based on Their Algebraic Representation in the Graph Model
Tóm tắt
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.
Tài liệu tham khảo
Bashar MA, Hipel KW, Kilgour DM (2012). Fuzzy preferences in the graph model for conflict resolution. IEEE Transactions on Fuzzy Systems 20(4):760–770.
Bashar MA, Hipel KW, Kilgour DM, Obeidi A (2017). Interval fuzzy preferences in the graph model for conflict resolution. Fuzzy Optimization and Decision Making 17(3):287–315.
Ben-Haim Y, Hipel KW (2002). The graph model for conflict resolution with information-gap uncertainty in preferences. Applied Mathematics and Computation 126(2-3):319–340.
Fang L, Hipel KW, Kilgour DM (1993). Interactive Decision Making: The Graph Model for Conflict Resolution. Wiley, New York.
Fraser NM, Hipel KW (1979). Solving complex conflicts. IEEE Transactions on Systems, Man, and Cybernetics 9(12): 805–817.
Fraser NM, Hipel KW (1984). Conflict Analysis: Models and Resolutions. Horth-Holland, New York.
Garcia A, Hipel KW (2017). Inverse engineering preferences in simple games. Applied Mathematics and Computation 311:184–194.
Hamouda L, Kilgour DM, Hipel KW (2004). Strength of preference in the graph model for conflict resolution. Group Decision and Negotiation 13(5):449–462.
Hamouda L, Kilgour DM, Hipel KW (2006). Strength of preference in graph models for multiple decision maker conflicts. Applied Mathematics and Computation 179(1):314–327.
Hipel KW, Fang L, Kilgour DM (1990). A formal analysis of the Canada-U.S. softwood lumber dispute. European Journal of Operation Research 46(2): 235–246.
Howard N (1971). Paradoxes of Rationality: Theory of Metagames and Political Behavior. Cambridge: MIT Press, MA.
Kilgour DM, Hipel KW, Fang L (1987). The graph model for conflicts. Automatica 23(1):41–55.
Kinsara RA, Kilgour DM, Hipel KW (2015). Inverse approach to the graph model for conflict resolution. IEEE Transactions on Systems, Man, and Cybernetics: Systems 45(5):734–742.
Kuang H, Bashar MA, Hipel KW, Kilgour DM (2015). Grey-based preference in a graph model for conflict resolution with multiple decision makers. IEEE Transactions on Systems, Man, and Cybernetics 45(9):1254–1267.
Li KW, Hipel KW, Kilgour DW, Fang L (2002). Stability definitions for 2-player conflict models with uncertain preferences. IEEE International Conference on Systems, Man, Cybernetics, Yasmine Hammamet, Tunisia, October 0609, 2002.
Li KW, Hipel KW, Kilgour DM, Fang L (2004). Preference uncertainty in the graph model for conflict resolution. IEEE Transactions on Systems, Man, and Cybernetics: Part A 34(4):507–520.
Li KW, Inohara T, Xu H (2014). Coalition analysis with preference uncertainty in group decision support. Applied Mathematics and Computation 231(1):307–319.
Nash JF (1950). Equilibrium points in n-person games. Proceedings of the National Academy of Sciences of the United States of America 36(1):48–49.
Nash JF (1951). Non-cooperative games. Annals of Mathematics 54(2):286–295.
Pianosi F, Beven K, Freeer J, et al (2016). Sensitivity analysis of environmental models: A systematic review with practical workflow. Environmental Modeling and Software 79:214–232.
Philpot S, Hipel KW, Johnson P (2016). Strategic analysis of a water rights conflict in the south western United States. Journal of Environmental Management 180(15):247–256.
Rego LC, dos Santos AM (2015). Probabilistic preferences in the graph model for conflict resolution. IEEE Transactions on Systems, Man, and Cybernetics: Systems 45(4):595–608.
Sakakibara H, Okada N, Nakase D (2002). The application of robustness analysis to the conflict with incomplete information. IEEE Transactions on Systems, Man, and Cybernetics: Part C 32(1):14–23.
Von Neumann J, Morgenstern O (1944). Theory of Games and Economic Behavior. Princeton: Princeton University Press, NJ.
Xu H, Hipel KW, Kilgour DM (2007). Matrix representation of conflicts with two decision-makers. IEEE International Proceedings on Systems, Man, and Cybernetics Montreal, Que. Canada, October 07–10, 2007.
Xu H, Hipel KW, Kilgour DM (2009). Matrix representation of solution concepts in multiple decision maker graph models. IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans 39(1):96–108.
Xu H, Hipel KW, Kilgour DM (2009). Multiple levels of preference in interactive strategic decisions. Discrete Applied Mathematics 57(15):3300–3313.
Xu H, Hipel KW, Kilgour DM, Fang L (2018). Conflict Resolution Using the Graph Model: Strategic Interactions in Competition and Cooperation. Springer.
Xu H, Kilgour DM, Hipel KW, Graeme Kemkes (2010). Using matrices to link conflict evolution and resolution in a graph model. European Journal of Operational Research 207(1):318–329.
Xu H, Hipel KW, Kilgour DM, Chen Y (2010). Combining strength and uncertainty for preferences in the graph model for conflict resolution with multiple decision makers. Theory and Decision 69(4): 497–521.
Zhao J, Xu H, Wang J (2017). Sensitivity of conflict analysis based on algebraic expression. Systems Engineering 35(7):153–158 (Chinese Journal).