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Rivalry is present in various spheres of human activity, for example, rivalry (competition) for a workplace, for a position, for the necessary resources, for a free place in transport and for points/grades in the educational process. The article is devoted to the issues of competition among students in educational activities for grades, including in the implementation of the point-rating system of assessment in educational institutions of higher education. According to various studies and based on the experience of the author’s professional activity, the use of a point-rating evaluation system in educational organizations has both its advantages and disadvantages. So, one of the indisputable advantages is considered to be an increase in students’ motivation for learning activities (to complete the task better than classmates), and one of the disadvantages is considered to be competition (sometimes unfair) for the assessment necessary for the student (often, this is a tough comparison with the scores received by classmates, and dissatisfaction (not corresponding to the real state of affairs) earned assessment, etc.). The significance of these points is enhanced due to the subjectivity of the teacher’s assessment of students, as well as the peculiarities of the distribution of points (individually for each teacher) and the evaluation of various creative educational works. Based on the study of the interaction of competing parties in educational activities for points, some methods are proposed, the use of which contributes to conscientious rivalry among students (joint gain, gain due to advantages), which indicates the practical significance of the article. The article shows that even with a detailed description and justification of the assessment (drawing up a scale and its criteria), various controversial issues will still arise in the assessment of students, leading to a certain form of rivalry in educational activities.