Strength of preference in graph models for multiple-decision-maker conflicts
Section snippets
Introduction and motivation
A conflict is a clash of interests, values, or actions. Conflicts arise naturally in human relationships at any level [1]. Strategic conflicts involve choices of action by several participants. The ubiquity of strategic conflicts in engineering management, business, and elsewhere in real life has motivated the development of formal conflict resolution methodologies to support the decision making process [2], [3]. In turn, computerized Decision Support Systems (DSSs) have been designed to enable
Expanded preference structure
Traditionally, a pair of binary relations {≻, ∼} on S expresses each DM’s relative preferences over states in the graph model, where s1 ≻ s2 indicates that s1 ∈ S is strictly preferred to s2 ∈ S and s1 ∼ s2 means that s1 ∈ S is indifferent to s2 ∈ S. The binary relation called “greatly preferred to”, ≫, indicates a DM’s strong preference for one state over another in such a way that the paired preference structure {≻, ∼} usually used in the graph model is extended to a triplet preference structure {≫, >, ∼},
General stability definitions
Fang et al. [14] define the solution concepts Nash, GMR, SMR, and SEQ for 2-DM and n-DM (n > 2) conflict models. The definitions presented next are for n-DM conflicts, and are built on the new notations introduced in Section 2.
Stability in an n-DM model requires that the possible responses by other DMs to a move by DM i ∈ N be examined. We begin by introducing the notion of a sanction sequence, which is relevant to the stability definitions GMR, SMR, and SEQ.
Suppose that H ⊆ N, H ≠ ∅, is any non-empty
Strong and weak solution concepts for n-decision-maker models
With strength of preference taken into account, stability can be defined as strong or weak according to the level of sanctioning. A unilateral improvement (UI) of a focal DM i is sanctioned strongly if it could result in a greatly less preferred state relative to i’s initial state (GMR and SEQ), and this sanction cannot be avoided by a counterresponse (SMR). Sanctions that produce mildly less preferred scenarios (GMR and SEQ), or that can be escaped from to mildly less preferred states (SMR),
The interrelationships of stability definitions
In a real-world conflict, knowledge of the theoretical links among different solution concepts can be very enlightening. For example, it has been proven that a state s satisfies , also satisfies , and [14]. Relationships among the Nash, GMR, SMR and SEQ solution concepts and their strong and weak extensions in the graph model framework are developed in this section.
Decision makers, options, and state transitions
The environmental dispute over the Garrison Diversion Unit (GDU) project took place between Canada and the United States in the 1970s. Fang et al. [14] carried out a strategic study of this dispute using the graph model, but did not take strength of preference into account.
The Garrison Diversion Unit (GDU) was a proposed irrigation project in the American state of North Dakota that involved the transfer of an immense amount of water from the Missouri River Basin to the Hudson Bay Basin, for use
Conclusions
The Graph Model for Conflict Resolution and its associated decision support system GMCR II constitute a flexible set of decision tools for addressing strategic issues arising in any field where humans make interactive decisions such as in engineering management, business, and policy analysis. In this paper, the classical binary preference structure is extended to a triplet of relations that accounts for strength of preference between states in an n-DM conflict situation which can be
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2023, Expert Systems with ApplicationsCitation Excerpt :Within the GMCR framework, preference strength and psychological considerations have also been incorporated. The concept of preference strength has been proposed and applied to GMCR by Hamouda, Kilgour, and Hipel (2004), Hamouda, Kilgour, and Hipel (2006). Xu, Hipel, Kilgour, and Chen (2010) have also proposed multiple levels of preferences and a hybrid preference framework that can be applied to GMCR.