Motivation and social aspects as interaction among teachers and students are essential for a competence-based learning process in an Open Distance Learning environment, and the goal in this article is to develop an interactive model to manage motivation between process’ participants. The article contains the concept of developing a motivation model aimed at supporting activity and cooperation of both the students and the teacher. The structure of the motivation model and formal assumptions are presented. The proposed model constitutes the theoretical formalization of the new situation, when a teacher and the students are obligated to elaborate on a didactic material repository content in accordance with the competence requirements. The mathematical method, based on game theory and simulation is suggested. Conditions for using simulation in the model are analysed in two simulated cases.