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

Abstract

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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Acknowledgements

The authors would like to thank the anonymous reviewers and the Associate Editor for their helpful comments which improved the quality of the paper. This work was supported by the National Natural Science Foundation of China (NSFC) (Grant Nos. 71971115, 71471087, and 61673209) and by the Natural Sciences and Engineering Research Council (NSERC) of Canada (Discovery Grant Nos. RGPIN-2017-04379 and RGPIN-2018-04345).

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Correspondence to Liping Fang.

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Han, Y., Xu, H., Fang, L. et al. An Integer Programming Approach to Solving the Inverse Graph Model for Conflict Resolution with Two Decision Makers. Group Decis Negot (2021). https://doi.org/10.1007/s10726-021-09755-w

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Keywords

  • Graph model for conflict resolution
  • Integer programming
  • Inverse analysis
  • Matrix representation
  • Stability definitions
  • Unknown preference