Stability Definitions: Simple Preference

Xu, Haiyan; Hipel, Keith W.; Kilgour, D. Marc; Fang, Liping

doi:10.1007/978-3-319-77670-5_4

Haiyan Xu⁶,
Keith W. Hipel^7,8,9,
D. Marc Kilgour^7,10 &
…
Liping Fang^7,11

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 153))

1562 Accesses

Abstract

Stability definitions describing a range of human behavior under conflict are presented for decision makers (DMs) having simple preferences in order to establish the concepts of stable states and equilibria in both the logical and matrix formulations of the Graph Model for Conflict Resolution (GMCR). For a DM with simple preference, a state or scenario is either more, less or equally preferred to another state in a conflict model. A state is stable for a DM if all of the DM’s available unilateral improvements can be blocked by specified patterns of countermoves by the other (sanctioning) DMs. The logical interpretation of GMCR, and the idea of interactive moves, are the basis of the four stability definitions presented in this chapter: Nash stability, general metarationality (GMR), symmetric metarationality (SMR) and sequential stability (SEQ). The logical definitions can be converted to equivalent matrix representations, which improve the computational performance of the engine of the decision support system described in Chap. 10. The contents of Chap. 3 provide background modeling for the definitions for this chapter, which in turn constitutes the launching pad for the preference structures built up in Chaps. 5, 6 and 7.

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Authors and Affiliations

College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu, China
Haiyan Xu
Department of Systems Design Engineering, University of Waterloo, Waterloo, ON, Canada
Keith W. Hipel, D. Marc Kilgour & Liping Fang
Centre for International Governance Innovation, Waterloo, ON, Canada
Keith W. Hipel
Balsillie School of International Affairs, Waterloo, ON, Canada
Keith W. Hipel
Department of Mathematics, Wilfrid Laurier University, Waterloo, ON, Canada
D. Marc Kilgour
Department of Mechanical and Industrial Engineering, Ryerson University, Toronto, ON, Canada
Liping Fang

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Haiyan Xu
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Keith W. Hipel
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D. Marc Kilgour
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Liping Fang
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Correspondence to Keith W. Hipel .

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Xu, H., Hipel, K.W., Kilgour, D.M., Fang, L. (2018). Stability Definitions: Simple Preference. In: Conflict Resolution Using the Graph Model: Strategic Interactions in Competition and Cooperation. Studies in Systems, Decision and Control, vol 153. Springer, Cham. https://doi.org/10.1007/978-3-319-77670-5_4

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DOI: https://doi.org/10.1007/978-3-319-77670-5_4
Published: 12 May 2018
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-77669-9
Online ISBN: 978-3-319-77670-5
eBook Packages: EngineeringEngineering (R0)

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