Mathematical formalization of agent conflict in achieving local goals

The article presents a mathematical formalization of the conflict interaction of active agents focused on achieving their local goals in the process of achieving the common goal of the organizational system. The conflict is considered as a clash of active agents over a single resource, the possession of which will allow achieving a local goal. Three types of relations of an active agent to a given resource (possession, non-distinction, opposition) are presented, taking into account their usefulness in achieving a local goal. Mathematically, the conflict between agents is determined by the establishment of links between the elements of the set of active agents with the elements of the set of resources that caused the conflict. An algorithm for evaluating the mutual impact of active agents due to a resource in the core of the conflict is proposed, based on the construction of a bipartite graph "active agent - resource" and a graph of conflict in the organizational system. The weights of the arcs of a bipartite graph are defined as the values of the utility functions of the resource that caused the conflict in achieving local goals by active agents. The implementation of the algorithm allows to obtain an assessment of the degree of collision of active agents due to a single resource and an assessment of the interaction of active agents in the core of the conflict. An example of the algorithm execution is given.

1. Wieviorka M. Social conflict. Current Sociology. 2013;61(5-6):696–713. https://doi.org/10.1177/0011392113499487

2. Liu J., Yu C., Li C., Han J. Cooperation or Conflict in Doctor-Patient Relationship? An Analysis From the Perspective of Evolutionary Game. IEEE Access. 2020;8:42898–42908. https://doi.org/10.1109/ACCESS.2020.2977385

3. Ismaili S., Fidanova S. Application of Intuitionistic Fuzzy Sets for Conflict Resolution Modeling and Agent Based Simulation. International Journal BIOautomation. 2019;23(2):175–184. https://doi.org/10.7546/ijba.2019.23.2.000544

4. Skowron A., Ramanna S., Peters J.F. Conflict Analysis and Information Systems: A Rough Set Approach. In: Rough Sets and Knowledge Technology: First International Conference, RSKT 2006: Proceedings, 24–26 July 2006, Chongquing, China. Berlin, Heidelberg: Springer; 2006. pp. 233–240. https://doi.org/10.1007/11795131_34

5. Sysoev D.V. Methods for analyzing canonical correlation pleiades in conflict relationships in social groups. Information technologies in construction, social and economic systems. 2020;(4):9–14. (In Russ.).

6. Khvostov A.A., Zhuravlev A.A., Zhuravlev E.A., Sysoev D.V. Mathematical model of conflict dynamics based on Markov chain. Information technologies in construction, social and economic systems. 2019;(3-4):30–35. (In Russ.).

7. Burkov V.N., Enaleev A.K., Korgin N.A. Incentive Compatibility and Strategy-Proofness of Mechanisms of Organizational Behavior Control: Retrospective, State of the Art, and Prospects of Theoretical Research. Automation and Remote Control. 2021;82(7):1119–1143. https://doi.org/10.1134/S0005117921070018

8. Burkov V.N., Burkova I.V., Daulbaeva Z.M., Khodunov A.M. Mekhanizmy stimulirovaniya pri raznykh tipakh povedeniya agentov. In: Upravlenie razvitiem krupnomasshtabnykh sistem MLSD’2019: Materialy dvenadtsatoi mezhdunarodnoi konferentsii, 01–03 October 2019, Moscow, Russia. Moscow: V.A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences; 2019. P. 1184. (In Russ.). https://doi.org/10.25728/mlsd.2019.1.1184

9. Rossikhina L.V., Betskov A.V., Makarov V.F., Kondratiev V.D. Mathematical modeling of relations between agents of an organizational system. Modeling, Optimization and Information Technology. 2024;12(4). (In Russ.). https://doi.org/10.26102/2310-6018/2024.47.4.001

10. Sysoev V.V. Conflict. Cooperation. Independence. Moscow: Moscow Academy of Economics and Law; 1999. 151 p. (In Russ.).