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The Graph Model for Conflict Resolution: Reflections on Three Decades of Development

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Abstract

The fundamental design and inherent capabilities of the Graph Model for Conflict Resolution (GMCR) to address a rich range of complex real world conflict situations are put into perspective by tracing its historical development over a period spanning more than 30 years, and highlighting great opportunities for meaningful future expansions within an era of artificial intelligence (AI) and intensifying conflict in an over-crowded world. By constructing a sound theoretical foundation for GMCR based upon assumptions reflecting what actually occurs in reality, a fascinating story is narrated on how GMCR was able to expand in bold new directions as well as take advantage of many important legacy decision technologies built within the earlier Metagame Analysis and later Conflict Analysis paradigms. From its predecessors, for instance, GMCR could benefit by the employment of option form put forward within Metagame Analysis for effectively recording a conflict, as well as preference elicitation techniques and solution concepts for defining chess-like behavior when calculating stability of states from the realm of Conflict Analysis. The key ideas outlined in the paper underlying the current and projected capabilities of GMCR include the development of four different ways to handle preference uncertainty in the presence of either transitive or intransitive preferences; a wide range of solution concepts for describing many kinds of human behavior under conflict; unique coalition analysis algorithms for determining if a given decision maker can fare better in a dispute via cooperation; tracing the evolution of a conflict over time; and the matrix formulation of GMCR for computational efficiency when calculating stability and also theoretically expanding GMCR in bold new directions. Inverse engineering is mentioned as an AI extension of GMCR for computationally determining the preferences required by decision makers in order to reach a desirable state, such as a climate change agreement in which all nations significantly cut back on their greenhouse gas emissions. The basic design of a decision support system for permitting researchers and practitioners to readily apply the foregoing and other advancements in GMCR to tough real world controversies is discussed. Although GMCR has been successfully applied to challenging disputes arising in many different fields, a simple climate change negotiation conflict between the US and China is utilized to explain clearly key concepts mentioned throughout the fascinating historical journey surrounding GMCR.

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References

  • Ali S, Xu H, Ahmed W, Ahmed N (2019a) Resolving strategic conflict for environmental conservation of glacial ecosystem: an attitudinal conflict resolution approach. Int J Glob Warm 18(3–4):221–238

    Google Scholar 

  • Ali S, Xu H, Al-amin AQ, Ahmed N (2019b) Energy sources choice and environmental sustainability disputes: an evolutional graph model approach. Qual Quan 53(2):561–581

    Google Scholar 

  • Aljefri YM, Bashar MA, Fang L, Hipel KW (2017) First level hypergame for investigating misperception in conflicts. IEEE T Syst Man Cy-Syst 48(12):2158–2175

    Google Scholar 

  • Aljefri YM, Hipel KW, Fang L (2018) General hypergame analysis within the graph model for conflict resolution. Oper Logist, Int J Syst Sci. https://doi.org/10.1080/23302674.2018.1476604

    Book  Google Scholar 

  • Al-Mutairi MS, Hipel KW, Kamel MS (2008a) Fuzzy preferences in conflicts. J Syst Sci Syst Eng 17(3):257–276

    Google Scholar 

  • Al-Mutairi MS, Hipel KW, Kamel MS (2008b) Trust and cooperation from a fuzzy perspective. Math Comput Simulat 6(2007):430–446

    Google Scholar 

  • Bashar MA, Kilgour DM, Hipel KW (2012) Fuzzy preferences in the graph model for conflict resolution. IEEE T Fuzzy Syst 20(4):760–770

    Google Scholar 

  • Bashar MA, Kilgour DM, Hipel KW (2014) Fuzzy option prioritization for the graph model for conflict resolution. Fuzzy Set Syst 26:34–48

    Google Scholar 

  • Bashar MA, Hipel KW, Kilgour DM, Obeidi A (2015) Coalition fuzzy stability analysis in the graph model for conflict resolution. J Intell Fuzzy Syst 29(2):593–607

    Google Scholar 

  • Bashar MA, Obeidi A, Kilgour DM, Hipel KW (2016) Modeling fuzzy and interval fuzzy preferences within a graph model framework. IEEE T Fuzzy Syst 24(4):765–778

    Google Scholar 

  • Bashar MA, Hipel KW, Kilgour DM, Obeidi A (2018) Interval fuzzy preferences in the graph model for conflict resolution. Fuzzy Optim Decis Ma 17(3):287–315

    Google Scholar 

  • Ben-Haim Y, Hipel KW (2002) The graph model for conflict resolution with information gap uncertainty in preferences. Appl Math Comput 126(2–3):319–340

    Google Scholar 

  • Bennett PG (1977) Toward a theory of hypergames. Omega 5(6):749–751

    Google Scholar 

  • Bennett PG (1980) Hypergames: developing a model of conflict. Futures 12(6):489–507

    Google Scholar 

  • Bennett PG, Dando MR (1979) Complex strategic analysis: a hypergame study of the fall of France. J Oper Res Soc 30(1):23–32

    Google Scholar 

  • Bernath Walker SG, Hipel KW, Inohara T (2009) Strategic decision making for improved environmental security: coalitions and attitudes in the graph model for conflict resolution. J Syst Sci Syst Eng 18(4):461–476

    Google Scholar 

  • Bernath Walker SG, Hipel KW, Inohara T (2012a) Dominating attitudes in the graph model for conflict resolution. J Syst Sci Syst Eng 21(3):316–336

    Google Scholar 

  • Bernath Walker SG, Hipel KW, Inohara T (2012b) Attitudes and preferences: approaches to representing decision maker desires. Appl Math Comput 218(12):6637–6647

    Google Scholar 

  • Brams SJ, Wittman D (1981) Nonmyopic equilibria in 2 × 2 games. Conflict Manag Peace 6(1):39–62

    Google Scholar 

  • Bryant JW (2003) The six dilemmas of collaboration: inter-organizational relationships as drama. Wiley, Chichester, UK

    Google Scholar 

  • Bryant JW (2015) Acting strategically using drama theory. CRC Press, Boca Raton

    Google Scholar 

  • Dagnino A, Hipel KW, Fraser NM (1989) Computer assistance in environmental mediation. Syst Prac 2(2):181–197

    Google Scholar 

  • Deng JL (1985) Grey incidence space in grey systems theory. Fuzzy Math 4(2):1–10

    Google Scholar 

  • Fang L, Hipel KW, Kilgour DM (1993) Interactive decision making: the graph model for conflict resolution. Wiley, New York

    Google Scholar 

  • Fang L, Hipel KW, Kilgour DM, Peng X (2003a) A decision support system for interactive decision making, part 1: model formulation. IEEE T Syst Man Cy Part C-Appl Rev 33(1):42–55

    Google Scholar 

  • Fang L, Hipel KW, Kilgour DM, Peng X (2003b) A decision support system for interactive decision making, part 2: analysis and output interpretation. IEEE T Syst Man Cy Part C-Appl Rev 33(1):56–66

    Google Scholar 

  • Fraser NM, Hipel KW (1979) Solving complex conflicts. IEEE T Syst Man Cy 9(12):805–816

    Google Scholar 

  • Fraser NM, Hipel KW (1980) Metagame analysis of the Poplar River conflict. J Oper Res Soc 31(5):377–385

    Google Scholar 

  • Fraser NM, Hipel KW (1984) Conflict analysis: models and resolutions. North-Holland, New York

    Google Scholar 

  • Fraser NM, Hipel KW (1988a) Decision support systems for conflict analysis. In: Proceedings of IMACS/IFOR first international colloquium on managerial decision support systems and knowledge-based systems, pp 13–21

  • Fraser NM, Hipel KW (1988b) Using Decision Maker: the conflict analysis program to resolve water resources conflicts. In: Rand GK (ed) Proc 11th Triennial Conference of the International Federation of Operations Research Societies (IFORS) and co-sponsored by the International Water Resources Association. North-Holland, Amsterdam, pp 522–535

    Google Scholar 

  • Garcia A, Hipel KW (2017) Inverse engineering preferences in simple games. Appl Math Comput 311:184–194

    Google Scholar 

  • Garcia A, Hipel KW, Obeidi A (2017) Water pricing conflict in British Columbia. Hydrol Res Letters 11(4):194–200

    Google Scholar 

  • Garcia A, Obeidi A, Hipel KW (2018a) Strategic advice for decision-making under conflict based on observed behaviour. Appl Math Comput 332:96–104

    Google Scholar 

  • Garcia A, Obeidi A, Hipel KW (2018b) Initial state stability for n-decision-maker conflicts. INFOR: Inform Syst Oper Res 57(2):226–241

    Google Scholar 

  • Garcia A, Obeidi A, Hipel KW (2019a) Inverse engineering preferences in the graph model for conflict resolution. IEEE T Syst Man Cy-Syst. https://doi.org/10.1109/TSMC.2018.2876589

    Article  Google Scholar 

  • Garcia A, Hipel KW, Obeidi A (2019b) Classifying metarational stabilities in conflicts. J Syst Sci Syst Eng 28(3):265–283

    Google Scholar 

  • Haimes YY (2016) Risk modeling, assessment, and management, 4th edn. Wiley, New York

    Google Scholar 

  • Haimes YY (2018) Modeling and managing interdependent complex systems of systems. Wiley-IEEE Press, Hoboken

    Google Scholar 

  • Hamouda L, Kilgour DM, Hipel KW (2004) Strength of preference in the graph model for conflict resolution. Group Decis Negot 13:449–462

    Google Scholar 

  • Hamouda L, Kilgour DM, Hipel KW (2006) Strength of preference in graph models for multiple decision-maker conflicts. Appl Math Comput 179(1):314–327

    Google Scholar 

  • He S, Kilgour DM, Hipel KW, Bashar MA (2013) A basic hierarchical graph model for conflict resolution with application to water diversion conflicts in China. INFOR: Inform Syst Oper Res 51(3):103–119

    Google Scholar 

  • He S, Hipel KW, Kilgour DM (2014) Water diversion conflicts in China: a hierarchical perspective. Water Resour Manag 28(7):1823–1837

    Google Scholar 

  • He S, Hipel KW, Kilgour DM (2017a) Analyzing market competition between Airbus and Boeing using a duo hierarchical model for conflict resolution. J Syst Sci Syst Eng 26(6):683–710

    Google Scholar 

  • He S, Kilgour DM, Hipel KW (2017b) A general hierarchical graph model for conflict resolution with application to greenhouse gas emission disputes between USA and China. Eur J Oper Res 257(3):919–932

    Google Scholar 

  • He S, Kilgour DM, Hipel KW (2018) A basic hierarchical model for conflict resolution with weighted preference. J Environ Inform 31(1):15–29

    Google Scholar 

  • Hipel KW (ed) (2009a) Conflict resolution, vol 1. Eolss Publishers, Oxford

    Google Scholar 

  • Hipel KW (ed) (2009b) Conflict resolution, vol 2. Eolss Publishers, Oxford

    Google Scholar 

  • Hipel KW (2011) A systems engineering approach to conflict resolution in command and control. Int C2J 5(1):1–56

    Google Scholar 

  • Hipel KW, Bernath Walker SG (2011) Conflict analysis in environmental management. Environmetrics 22:279–293

    Google Scholar 

  • Hipel KW, Fang L (2005) Multiple participant decision making in societal and technological systems. Systems and Human Science, for Safety, Security, and Dependability: Selected Papers of the 1st International Symposium SSR2003, Osaka, Japan, November 2003. Elsevier, Amsterdam, pp 3–31

    Google Scholar 

  • Hipel KW, Fraser NM (1980) Metagame analysis of the Garrison conflict. Water Resour Res 16(4):629–637

    Google Scholar 

  • Hipel KW, Meister DBG (1994) Conflict analysis methodology for modelling coalition in multilateral negotiations. Inform Decis Technol 19(2):85–103

    Google Scholar 

  • Hipel KW, Wang M, Fraser NM (1988) Hypergame analysis of the Falklands/Malvinas conflict. Int Stud Quart 32:335–358

    Google Scholar 

  • Hipel KW, Fang L, Kilgour DM, Haight M (1993) Environmental conflict resolution using the graph model. In: Proceedings of the 1993 IEEE international conference on systems, man, and cybernetic, pp 153–158. https://doi.org/10.1109/icsmc.1993.384737

  • Hipel KW, Kilgour DM, Fang L, Peng X (1997) The decision support system GMCR in environmental conflict management. Appl Math Comput 83(2–3):117–152

    Google Scholar 

  • Hipel KW, Fang L, Kilgour DM (2008a) Decision support systems in water resources and environmental management. J Hydrol Eng 13(9):761–770

    Google Scholar 

  • Hipel KW, Obeidi A, Fang L, Kilgour DM (2008b) Adaptive systems thinking in integrated water resources management with insights into conflicts over water exports. INFOR 46(1):51–69

    Google Scholar 

  • Hipel KW, Kilgour DM, Rajabi S, Chen Y (2009a) Operations research and refinement of courses of action. In: Sage AP, Rouse WB (eds) Handbook of systems engineering and management, 2nd edn. Wiley, New York, pp 1171–1222

    Google Scholar 

  • Hipel KW, Obeidi A, Fang L, Kilgour DM (2009b) Sustainable environmental management from a system of systems perspective. In: Jamshidi M (ed) System of systems engineering: innovations for the 21st century. Wiley, New York, pp 443–481

    Google Scholar 

  • Hipel KW, Kilgour DM, Fang L (2011a) The graph model for conflict resolution. In: Cochran JJ (Editor-in-Chief) with Cox LA, Keskinocak P, Kharoufeh JP, Smith JC (area eds) Wiley encyclopedia of operations research and management science, vol 3. Wiley, New York, pp 2099–2111

  • Hipel KW, Kilgour DM, Bashar MA (2011b) Fuzzy preferences in multiple participant decision making. Sci Iran Trans D-Comput Sci Eng Electr Eng 18(3(D1)):627–638

    Google Scholar 

  • Hipel KW, Sakamoto M, Hagihara Y (2015) Third party intervention in conflict resolution: dispute between Bangladesh and India over control of the Ganges river. In: Hagihara K, Asahi C (eds) Coping with regional vulnerability: preventing and mitigating damages from environmental disasters. Springer Japan KK, Tokyo, pp 329–355

    Google Scholar 

  • Howard N (1971) Paradoxes of rationality: theory of metagames and political behavior. MIT Press, Cambridge

    Google Scholar 

  • Howard N (1994a) Drama theory and its relations to game theory. Part 1: dramatic resolution. Group Decis Negot 3(2):187–206

    Google Scholar 

  • Howard N (1994b) Drama theory and its relations to game theory. Part 2: formal model of the resolution process. Group Decis Negot 3(2):207–235

    Google Scholar 

  • Howard N (1999) Confrontation analysis: how to win operations other than war, The Command and Control Research Project (CCRP). The Pentagon, Washington, DC

    Google Scholar 

  • Inohara T (2016) State transition time analysis in the graph model for conflict resolution. Appl Math Comput 274:372–382

    Google Scholar 

  • Inohara T, Hipel KW (2008a) Coalition analysis in the graph model for conflict resolution. Syst Eng 11(4):343–359

    Google Scholar 

  • Inohara T, Hipel KW (2008b) Interrelationships among noncooperative and coalition stability concepts. J Syst Sci Syst Eng 17(1):1–29

    Google Scholar 

  • Inohara T, Hipel KW, Bernath Walker SG (2007) Conflict analysis approaches for investigating attitudes and misperceptions in the war of 1812. J Syst Sci Syst Eng 16(2):181–201

    Google Scholar 

  • Ke Y, Fu B, De M, Hipel KW (2012a) A hierarchical multiple criteria model for eliciting relative preferences in conflict situations. J Syst Sci Syst Eng 21(1):56–76

    Google Scholar 

  • Ke Y, Li KW, Hipel KW (2012b) An integrated multiple criteria preference ranking approach to the Canadian west coast port congestion problem. Expert Syst Appl 39(10):9181–9190

    Google Scholar 

  • Kilgour DM (1984) Equilibria for far-sighted players. Theor Decis 16(2):135–157

    Google Scholar 

  • Kilgour DM (1985) Anticipation and stability in two-person noncooperative games. In: Ward MD, Luterbacher U (eds) Dynamic models of international conflict. Lynne Rienner Press, Boulder, CO, pp 26–51

    Google Scholar 

  • Kilgour DM, Eden C (2010) Handbook of group decision and negotiation. Springer, Dordrecht

    Google Scholar 

  • Kilgour DM, Hipel KW (2005) The graph model for conflict resolution: past, present, and future. Group Decis Negot 14(6):441–460

    Google Scholar 

  • Kilgour DM, Hipel KW, Fang L (1987) The graph model for conflicts. Automatica 23(1):41–55

    Google Scholar 

  • Kilgour DM, Hipel KW, Fang L, Peng X (2001) Coalition analysis in group decision support. Group Decis Negot 10(2):159–175

    Google Scholar 

  • Kinsara RA, Kilgour DM, Hipel KW (2015a) Inverse approach to the graph model for conflict resolution. IEEE T Syst Man Cy-Syst 45(5):734–742

    Google Scholar 

  • Kinsara RA, Petersons O, Hipel KW, Kilgour DM (2015b) Advanced decision support system for the graph model for conflict resolution. J Decis Syst 24(2):117–145

    Google Scholar 

  • Kinsara RA, Kilgour DM, Hipel KW (2018) Communication features in a DSS for conflict resolution based on the graph model. Int J Inform Decis Sci 10(1):39–56

    Google Scholar 

  • Kuang H, Bashar MA, Hipel KW, Kilgour DM (2015a) Grey-based preference in a graph model for conflict resolution with multiple decision makers. IEEE T Syst Man Cy-Syst 45(9):1254–1267

    Google Scholar 

  • Kuang H, Bashar MA, Kilgour DM, Hipel KW (2015b) Strategic analysis of a brownfield revitalization conflict using the grey-based graph model for conflict resolution. Eur J Decis Process 3(3):219–248

    Google Scholar 

  • Kuang H, Kilgour DM, Hipel KW (2015c) Grey-based PROMETHEE II with application to evaluation of source water protection strategies. Inform Sci 294:376–389

    Google Scholar 

  • Kuhn JRD, Hipel KW, Fraser NM (1983) A coalition analysis algorithm with application to the Zimbabwe conflict. IEEE T Syst Man Cy 13(3):338–352

    Google Scholar 

  • Levy JK, Hipel KW, Howard N (2009a) Advances in drama theory for managing global hazards and disasters, part 1: theoretical foundation. Group Decis Negot 18(4):303–316

    Google Scholar 

  • Levy JK, Hipel KW, Howard N (2009b) Advances in drama theory for managing global hazards and disasters, part 2: coping with global climate change and environmental catastrophe. Group Decis Negot 18(4):317–334

    Google Scholar 

  • Li KW, Hipel KW, Kilgour DM, Fang L (2004) Preference uncertainty in the graph model for conflict resolution. IEEE T Syst Man Cy Part A-Syst Hum 34(4):507–520

    Google Scholar 

  • Li KW, Kilgour DM, Hipel KW (2005) Status quo analysis in the graph model for conflict resolution. J Oper Res Soc 56:699–707

    Google Scholar 

  • Madani K (2013) Modeling international climate change negotiations more responsibly: can highly simplified game theory models provide reliable policy insights? Ecol Econ 90:68–76

    Google Scholar 

  • Madani K, Hipel KW (2011) Non-cooperative stability definitions for strategic analysis of generic water resources conflicts. Water Resour Manage 25(8):1949–1977

    Google Scholar 

  • Meister DBG, Hipel KW, De M (1992) Coalition formation. J Sci Ind Res 51(8–9):612–625

    Google Scholar 

  • Nash JF (1950) Equilibrium points in n-person games. Proc Natl Acad Sci 36(1):48–49

    Google Scholar 

  • Nash JF (1951) Non-cooperative games. Ann Math 54(2):286–295

    Google Scholar 

  • Obeidi A, Hipel KW (2005) Strategic and dilemma analyses of a water export conflict. INFOR 43(3):247–270

    Google Scholar 

  • Obeidi A, Hipel KW, Kilgour DM (2005) The role of emotions in envisioning outcomes in conflict analysis. Group Decis Negot 14(6):481–500

    Google Scholar 

  • Obeidi A, Kilgour DM, Hipel KW (2009a) Perceptual stability analysis of a graph model system. IEEE T Syst Man Cy Part A-Syst Hum 39(5):993–1006

    Google Scholar 

  • Obeidi A, Kilgour DM, Hipel KW (2009b) Perceptual graph model systems. Group Decis Negot 18(3):261–277

    Google Scholar 

  • Peng X, Hipel KW, Kilgour DM, Fang L (1997) Representing ordinal preferences in the decision support system GMCR II. In: Proceedings of 1997 IEEE international conference on systems, man, and cybernetic, pp 809–814. https://doi.org/10.1109/icsmc.1997.626196

  • Rêgo LC, dos Santos AM (2015) Probabilistic preferences in the graph model for conflict resolution. IEEE T Syst Man Cy-Syst 45(4):595–608

    Google Scholar 

  • Rêgo LC, dos Santos AM (2018) Upper and lower probabilistic preferences in the graph model for conflict resolution. Int J Approximate Reasoning 98:96–111

    Google Scholar 

  • Rêgo LC, Vieira GIA (2017a) Interactive unawareness in the graph model for conflict resolution. IEEE T Syst Man Cy-Syst. https://doi.org/10.1109/TSMC.2017.2729279

    Article  Google Scholar 

  • Rêgo LC, Vieira GIA (2017b) Symmetric sequential stability in the graph model for conflict resolution with multiple decision makers. Group Decis Negot 26(4):775–792

    Google Scholar 

  • Rêgo LC, Vieira GIA (2019a) Maximinh stability in the graph model for conflict resolution for bilateral conflicts. IEEE T Syst Man Cy-Syst. https://doi.org/10.1109/TSMC.2019.2917824

    Article  Google Scholar 

  • Rêgo LC, Vieira GIA (2019b) Probabilistic option prioritizing in the graph model for conflict resolution. Group Decis Negot 28(6):1149–1165

    Google Scholar 

  • Ross S, Fang L, Hipel KW (2002) A case-based reasoning system for conflict resolution: design and implementation. Eng Appl Artif Intell 15(3–4):369–383

    Google Scholar 

  • Sage AP (1991) Decision support systems engineering. Wiley, New York

    Google Scholar 

  • Sakakibara H, Okada N, Nakase D (2002) The application of robustness analysis to the conflict with incomplete information. IEEE T Syst Man Cy Part C-Appl Rev 32(1):14–23

    Google Scholar 

  • Shupe MC, Wright WM, Hipel KW, Fraser NM (1980) Nationalization of the Suez Canal: a hypergame analysis. J Conflict Resolut 24(3):477–493

    Google Scholar 

  • Silva MM, Kilgour DM, Hipel KW, Costa APCS (2017) Probabilistic composition of preferences in the graph model with application to the New Recife project. J Legal Aff Dispute Resolut Eng Constr 9(3):05017004. https://doi.org/10.1061/(ASCE)LA.1943-4170.0000235

    Article  Google Scholar 

  • Stokes NW, Hipel KW, Roe PH (1985) The New York subway car dispute. INFOR 23(2):51–68

    Google Scholar 

  • Takahashi MA, Fraser NM, Hipel KW (1984) A procedure for analysing hypergames. Eur J Oper Res 18(1):111–122

    Google Scholar 

  • Von Neumann J (1928) Zur theorie der gesellschaftsspiele (On the theory of parlor games). Math Ann 100(1):295–320. https://doi.org/10.1007/bf01448847

    Article  Google Scholar 

  • Von Neumann J, Morgenstern O (1944) Theory of games and economic behavior. Princeton University Press, Princeton

    Google Scholar 

  • Von Neumann J, Morgenstern O (1953) Theory of games and economic behavior, 3rd edn. Princeton University Press, Princeton

    Google Scholar 

  • Wang M, Hipel KW, Fraser NM (1988) Modelling misperceptions in games. Behav Sci 33(3):207–223

    Google Scholar 

  • Wang J, Hipel KW, Fang L, Dang Y (2018) Matrix representations of the inverse problem in the graph model for conflict resolution. Eur J Oper Res 270(1):282–293

    Google Scholar 

  • Wang J, Hipel KW, Fang L, Xu H, Kilgour DM (2019) Behavioural analysis in the graph model for conflict resolution. IEEE T Syst Man Cy-Syst 49(5):904–916

    Google Scholar 

  • Wright WM, Shupe MC, Fraser NM, Hipel KW (1980) A conflict analysis of the Suez Canal invasion of 1956. Conflict Manage Peace Sci 5(1):27–40

    Google Scholar 

  • Wu Z, Xu H, Ke GY (2019) The strategy of third-party mediation based on the option prioritization in the graph model. J Syst Sci Syst Eng 28(4):399–414

    Google Scholar 

  • Xu H, Hipel KW, Kilgour DM (2008) Preference strength and uncertainty in the graph model for conflict resolution for two decision-makers. In: Proceedings of 2008 IEEE international conference on systems, man, and cybernetic, pp 2907–2912

  • Xu H, Hipel KW, Kilgour DM (2009a) Multiple levels of preference in interactive strategic decisions. Discrete Appl Math 157(15):3300–3313

    Google Scholar 

  • Xu H, Hipel KW, Kilgour DM (2009b) Matrix representation of solution concepts in multiple decision maker graph models. IEEE T Syst Man Cy Part A-Syst Hum 39(1):96–108

    Google Scholar 

  • Xu H, Hipel KW, Kilgour DM, Chen Y (2010a) Combining strength and uncertainty for preferences in the graph model for conflict resolution with multiple decision makers. Theor Decis 69(4):497–521

    Google Scholar 

  • Xu H, Kilgour DM, Hipel KW (2010b) Matrix representation and extension of coalition analysis in group decision support. Comput Math Appl 60(5):1164–1176

    Google Scholar 

  • Xu H, Kilgour DM, Hipel KW (2011) Matrix representation of conflict resolution in multiple-decision-maker graph models with preference uncertainty. Group Decis Negot 20(6):755–779

    Google Scholar 

  • Xu H, Hipel KW, Kilgour DM, Fang L (2018a) Conflict resolution using the graph model: strategic interactions in competition and cooperation. Springer, Cham

    Google Scholar 

  • Xu H, Liu G, Kilgour DM, Hipel KW (2018b) Stackelberg stability in the graph model for conflict resolution: Definition and implementation. In: Jiang X, Xu H, He S, Ke GY (eds) Proceedings of the 2018 international conference on group decisions and negations, pp 188–193

  • Xu P, Xu H, Ke GY (2018c) Integrating an option-oriented attitude analysis into investigating the degree of stabilities in conflict resolution. Group Decis Negot 27(6):981–1010

    Google Scholar 

  • Xu H, Zhao J, Ke GY, Ali S (2019) Matrix representation of consensus and dissent stabilities in the graph model for conflict resolution. Discrete Appl Math 259:205–217

    Google Scholar 

  • Yousefi S, Hipel KW, Hegazy T (2010a) Considering attitudes in strategic negotiation over brownfield disputes. ASCE J Legal Aff Dispute Resolut Eng Constr 2(4):1–10

    Google Scholar 

  • Yousefi S, Hipel KW, Hegazy T (2010b) Attitude-based strategic negotiation for conflict management in construction projects. Proj Manag J 41(4):99–107

    Google Scholar 

  • Yousefi S, Hipel KW, Hegazy T (2010c) Attitude-based negotiation methodology for the management of construction disputes. J Manag Eng 26:114–122

    Google Scholar 

  • Yu J, Kilgour DM, Hipel KW, Zhao M (2015) Power asymmetry in conflict resolution with application to a water pollution dispute in China. Water Resour Res 51(10):8627–8645

    Google Scholar 

  • Zadeh LA (1965) Fuzzy sets. Inform Control 8(3):338–353

    Google Scholar 

  • Zagare FC (1984) Limited-move equilibria in 2 × 2 games. Theor Decis 16(1):1–19

    Google Scholar 

  • Zeng DZ, Fang L, Hipel KW, Kilgour DM (2005) Policy stable states in the graph model for conflict resolution. Theor Decis 57:345–365

    Google Scholar 

  • Zeng DZ, Fang L, Hipel KW, Kilgour DM (2006) Generalized metarationalities in the graph model for conflict resolution. Discrete Appl Math 154(16):2430–2443

    Google Scholar 

  • Zeng DZ, Fang L, Hipel KW, Kilgour DM (2007) Policy equilibrium and generalized metarationalities for multiple decision-maker conflicts. IEEE T Syst Man Cy Part A-Syst Hum 37(4):456–463

    Google Scholar 

  • Zhao S, Xu H (2017) Grey option prioritization for the graph model for conflict resolution. J Grey Syst 29(3):14–25

    Google Scholar 

  • Zhao S, Xu H, Hipel KW, Fang L (2019a) Mixed stabilities for analyzing opponents’ heterogeneous behavior within the graph model for conflict resolution. Eur J Oper Res 277(2):621–632

    Google Scholar 

  • Zhao S, Xu H, Hipel KW, Fang L (2019b) Mixed coalitional stabilities with full participation of sanctioning opponents within the graph model for conflict resolution. IEEE T Syst Man Cy-Syst. https://doi.org/10.1109/TSMC.2019.2950673

    Article  Google Scholar 

  • Zhu Z, Kilgour DM, Hipel KW (2018) A new approach to coalition analysis within the graph model. IEEE T Syst Man Cy-Syst. https://doi.org/10.1109/TSMC.2018.2811402

    Article  Google Scholar 

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Acknowledgements

The authors feel highly privileged to have worked with many talented graduate students and colleagues from Canada and around the globe on research topics connected to the theory and practice of GMCR. Many of the papers cited in this article were written jointly with other researchers while other referenced work did not involve the authors. The academic home at which they completed much of their GMCR research is the Conflict Analysis Group located in the Department of Systems Design Engineering at the University of Waterloo. The authors would like to express their sincere appreciation to Dr. Yi Xiao, a Postdoctoral Fellow within the Conflict Analysis Group and its Executive Manager (2017 to 2019), for his timely advice and work in preparing the current paper. Ms. Yu (Jasmine) Han, an International Visiting Graduate Student within the Conflict Analysis Group (November 2018 to November 2019) who is from the Nanjing University of Aeronautics and Astronautics in China where she is a Ph.D. student, kindly assisted the authors to incorporate reviewers’ comments into this paper. They are also grateful to Mrs. Sheila Hipel for carefully reading many versions of the paper to enhance its presentation quality. They are thankful to a number of professional organizations for sponsoring academic journals and conferences in which papers dealing with GMCR were published and presented over many years. These include the Group Decision and Negotiation Section of INFORMS (The Institute for Operations Research and the Management Sciences) which is affiliated with the Springer journal Group Decision and Negotiation and hosts an annual international conference, as well as the IEEE Systems, Man and Cybernetics Society which publishes the journal named the IEEE Transactions on Systems, Man and Cybernetics: Systems and holds a yearly international conference. The authors have organized special sessions on conflict resolution at all international GDN and SMC conferences since 2001 and 1991, respectively. Special sessions on conflict resolution have been included in all conferences sponsored by the International Conferences on Water Resources and Environment Research (ICWRER) since the founding of this sequence of conferences at Waterloo in 1993. The research appearing in this paper and other published work involving the authors were funded by Discovery Grants separately held by the authors from the Natural Sciences and Engineering Research Council (NSERC) of Canada (Grant Nos. RGPIN-2018-04345, RGPIN-2017-04379). Finally, the authors would like to express their gratitude to anonymous referees whose suggestions improved the quality of their paper.

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Authors and Affiliations

  1. Department of Systems Design Engineering, University of Waterloo, Waterloo, ON, N2L 3G1, Canada

    Keith W. Hipel, Liping Fang & D. Marc Kilgour

  2. Balsillie School of International Affairs, Waterloo, ON, N2L 6C2, Canada

    Keith W. Hipel

  3. Centre for International Governance Innovation, Waterloo, ON, N2L 6C2, Canada

    Keith W. Hipel

  4. Department of Mechanical and Industrial Engineering, Ryerson University, Toronto, ON, M5B 2K3, Canada

    Liping Fang

  5. Department of Mathematics, Wilfrid Laurier University, Waterloo, ON, N2L 3C5, Canada

    D. Marc Kilgour

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  1. Keith W. Hipel
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  2. Liping Fang
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  3. D. Marc Kilgour
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Correspondence to Liping Fang.

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Hipel, K.W., Fang, L. & Kilgour, D.M. The Graph Model for Conflict Resolution: Reflections on Three Decades of Development. Group Decis Negot 29, 11–60 (2020). https://doi.org/10.1007/s10726-019-09648-z

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