Dynamic model of evaluation with corruption

A model of interaction between a professor and a student with possible corruption is studied in the game-theoretic setting. The model is formalized as a two-person game in extended form with perfect information. It is assumed that students have high or low qualification only. At the same time, corruption will manifest itself in the form of capture in the case of a low qualified student and in the form of extortion for students with high qualification. The decision is made by the method of backward induction using the Kuhn algorithm for analyzing the game in an extended form. This algorithm is based on analysis of the values of payoffs of the control subjects by the method of backward induction. An algorithm for constructing the solution is given. Simulation modeling is carried out based on the values of the payoffs of the control subjects. The results of numerical experiments are presented and analyzed. The meaningful conclusions are made on the base of the analysis of the results of simulation experiments in the case of a student of high and low qualification. The main conclusion is as follows. In the case of highly qualified students, one reduction in their moral costs when filing complaints about corrupt behavior of a professor is enough to eliminate corruption in a professor – student system. In the case of a low qualified student, it is more difficult to eradicate corruption. This requires a comprehensive approach that involves a significant increase in the amount of the professor's punishment for a bribe, as well as his payoffs in a non-corrupt case, and increasing the probability of detecting the fact of a bribe by strengthening administrative control over a professor.