An Integer Programming Approach to Solving the Inverse Graph Model for Conflict Resolution with Two Decision Makers

Operational algorithms for solving the inverse problem for the graph model for conflict resolution are presented for the case of two decision makers (DMs) under a variety of solution concepts, including Nash stability (Nash), general metarationality (GMR), symmetric metarationality (SMR), and sequen...

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Bibliographic Details
Published in:Group decision and negotiation Vol. 31; no. 1; pp. 23 - 48
Main Authors: Han, Yu, Xu, Haiyan, Fang, Liping, Hipel, Keith W.
Format: Journal Article
Language:English
Published: Dordrecht Springer Netherlands 01.02.2022
Springer Nature B.V
Subjects:
Algorithms
Biological and Physical Anthropology
Business and Management
Conflict resolution
Decision makers
Decision making
Integer programming
Linear programming
Nonlinear programming
Usefulness
Integer programming
Inverse analysis
Stability definitions
Matrix representation
Graph model for conflict resolution
Unknown preference
ISSN:0926-2644, 1572-9907
Online Access:Get full text
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Summary:Operational algorithms for solving the inverse problem for the graph model for conflict resolution are presented for the case of two decision makers (DMs) under a variety of solution concepts, including Nash stability (Nash), general metarationality (GMR), symmetric metarationality (SMR), and sequential stability (SEQ). The algorithms based on integer programming enable a DM, an analyst, or a mediator to obtain all of the preferences required to make a specified state to be an equilibrium or resolution. For the cases of Nash, GMR, and SMR, the respective inverse algorithm for the focal DM is formulated as a 0–1 integer linear programming problem even when both DMs’ preferences are unknown. For the situation of SEQ, when both DMs’ preferences are unknown, the focal DM’s algorithm is a 0–1 integer nonlinear programming problem while, under the condition that the opponent’s preferences are known, the focal DM’s 0–1 integer programming problem is linear. The usefulness of the algorithms developed is demonstrated by applying them to an illustrative dispute.
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ISSN:0926-2644
1572-9907
DOI:10.1007/s10726-021-09755-w