Game-Theoretic Models of Quality Management in Organizations under Corruption

Abstract

We consider game theoretic models of the quality management in an organizational system under corruption. A graph theoretic formalization of the process approach in quality management is proposed. In a static case, a problem of quality management in a two-level organizational system under corruption is formalized as an inverse Stackelberg game with an additional viability condition. It is solved by means of Germeier theorem. In a three-level model we analyze how the Principal can constraint corruption by penalties. The conditions under which the Principal rather supports corruption than constraints it are determined. In a dynamic case, a quality indicator is considered as a state variable which changes in a discrete time due to an equation of dynamics. A two-level model of the type "supervisor-agent" is studied first. It is assumed that a quality requirement is obligatory for the agent but he can weaken this requirement in exchange for a bribe to the supervisor. Then we build and analyze a three-level model by adding the Principal that can charge penalties to other players if a bribe is found. The game theoretic models are investigated numerically by means of simulation modeling.