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Stackelberg Stability in the Graph Model for Conflict Resolution: Definition and Implementation

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Innovation for Systems Information and Decision (INSID 2020)

Part of the book series: Lecture Notes in Business Information Processing ((LNBIP,volume 405))

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Abstract

This paper proposes a new algebraic definition that facilities calculating of Stackelberg stability in a graph model for conflict resolution with two decision makers. Most stability definitions used in the graph model methodology place decision makers at the same level, in the sense that their roles are symmetric. In practice, however, one decision maker may join by forcing the other to respond to his or her decision. So, to be applied, a model must specify the leader and the follower. Stackelberg stability can be defined logically, but an algorithm to implement it has not been developed until now, due to its complicated recursive formula. To permit Stackelberg stability to be calculated efficiently and encoded conveniently, within a decision support system, an algebraic test for the stability is developed. This algebraic representation of Stackelberg stability is easy to implement and interpret. A superpower military confrontation is used to illustrate how Stackelberg stability can be employed to a real-world application using the new approach.

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Acknowledgement

The authors appreciate financial support from the National Natural Science Foundation of China (71971115, 71471087) and National Social Science Foundation of China (12AZD102).

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Authors and Affiliations

  1. College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu, China

    Haiyan Xu & Guixian Liu

  2. School of Mathematics and Information Science, Henan polytechnic University, Jiaozuo, China

    Guixian Liu

  3. Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario, N2L 3C5, Canada

    D. Marc Kilgour

  4. Department of Systems Design Engineering, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada

    Keith W. Hipel

Authors
  1. Haiyan Xu
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  2. Guixian Liu
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  3. D. Marc Kilgour
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  4. Keith W. Hipel
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Corresponding author

Correspondence to Haiyan Xu .

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Editors and Affiliations

  1. Federal Univ of Pernambuco, Recife, Pernambuco, Brazil

    Adiel Teixeira de Almeida

  2. Departamento de Engenharia de Producao, Universidade Federal de Pernambuco, Recife, Pernambuco, Brazil

    Danielle Costa Morais

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Xu, H., Liu, G., Kilgour, D.M., Hipel, K.W. (2020). Stackelberg Stability in the Graph Model for Conflict Resolution: Definition and Implementation. In: de Almeida, A.T., Morais, D.C. (eds) Innovation for Systems Information and Decision. INSID 2020. Lecture Notes in Business Information Processing, vol 405. Springer, Cham. https://doi.org/10.1007/978-3-030-64399-7_6

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  • DOI: https://doi.org/10.1007/978-3-030-64399-7_6

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  • Print ISBN: 978-3-030-64398-0

  • Online ISBN: 978-3-030-64399-7

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