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

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.