Construction and application of hyper-inverse conflict models based on the sequential stability
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Construction and application of hyper‑inverse conflict models based on the sequential stability Yu Han1 · Haiyan Xu1 · Ginger Y. Ke2 Received: 5 October 2019 / Accepted: 7 September 2020 © EURO - The Association of European Operational Research Societies and Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Based on the graph model for conflict resolution (GMCR), an analytical framework is proposed to assist the focal decision maker (DM) with an informational advantage in resolving real-world hyper-inverse conflict situations considering the sequential (SEQ) stability. The hyper-inverse conflict resolution aims to obtain the opponent’s misunderstanding preferences of focal DM, which can assist the focal DM in taking the initiative in a conflict. Among all stabilities in GMCR, the SEQ stability is selected in the present study, because this stability concept provides a logical basis for a DM to sanction the opponent, which reflects the case for many conflicts. Moreover, a nonlinear binary optimization model rooted in the matrix representation of SEQ stability is constructed to capture the cause and process of the abnormal individual stability (or stabilities) in the hypergame. Then, a solution procedure is designed for solving the optimization model to obtain the preferences that are misunderstood by the opponent. Finally, an illustrative example of two DMs in an environmental management conflict is studied to demonstrate how the proposed framework can be conveniently employed in practice. Keywords Graph model for conflict resolution · Inverse problem · Hypergame · Sequential stability · Nonlinear binary programming model Mathematics Subject Classification 91-10
1 Introduction Conflicts inevitably arise whenever human beings interact with one another. From minor differences in opinions to deadly confrontations, people seek possible resolutions when facing conflicts. The graph model for conflict resolution (GMCR) is * Ginger Y. Ke [email protected] 1
College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing, China
2
Faculty of Business Administration, Memorial University of Newfoundland, St. John’s, Canada
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a flexible powerful tool that can be used to analyse and resolve real-world conflict situations, where independent DMs interact with each other to achieve one of many possible outcomes over DMs’ preferences (Xu et al. 2010; Wang et al. 2015). The investigation process of the Standard GMCR (Fang et al. 1993; Kilgour et al. 1990, 1987; Xu et al. 2008, 2018a) is to examine the involved parties and their individual options and preferences via various stability definitions. The stability definitions used in GMCR are linked to DMs’ preferences and behaviours. For example, the main definitions include the Nash stability (Nash 1950), general metarationality (GMR) (Howard 1971), symmetric metarationality (SMR) (Howard 1971), and sequential (SEQ) stability (Fraser and Hipel 1979). The SEQ stability among all stabilities in
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