On the Performance of Managers and Controllers: A Polymatrix Game Approach for the Manager–Controller–Board of Directors’ Conflict

  • S. Belhaiza
  • S. Charrad
  • R. M’Hallah


In this article, we focus on the conflict among the manager, the controller and the board of directors of a company. We model the problem as a three-player polymatrix game. Under a set of assumptions, we identify five potential Nash equilibria. We prove that the Nash equilibrium is unique, despite its changing structure. Next, we analyze the influence of the manager’s and controller’s bonuses and penalties on the Nash equilibria. Finally, we explain how the manager and the controller may decrease or maintain their performance, when their bonuses or penalties increase.


Game theory Polymatrix game Nash equilibrium Manager–controller–board of directors’ conflict 

Mathematics Subject Classification

49J53 49K99 


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsKing Fahd University of Petroleum and MineralsDhahranKingdom of Saudi Arabia
  2. 2.Department of Finance and Management Science, Community CollegeImam Abdulrahman Bin Faisal UniversityDammamKingdom of Saudi Arabia
  3. 3.Department of Statistics and Operations Research, College of ScienceKuwait UniversityKuwait CityKuwait

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