The quality of education in higher education concerns both the process of education and higher education as a good produced as a result of education processes. In the last several dozen years, the quality of education has become a major issue dealt with as part of public policy in the area of higher education both in the dimension of particular countries participating in the Bologna Process, and in the European Higher Education Area. As a result, social sciences have shown more interest in education processes in higher education, with managing the quality of education becoming one of the ideas central to the matter. Studies into the quality of education are conducted nowadays by representatives of many social sciences, adopting many different research approaches. The research approach proposed in this article refers to the organisational game concept and draws on the assumptions and the notional apparatus of the so-called decision-making approach as regards making public decisions. A particular assumption that has been made is that the activity of entities involved in the process of education and performing different roles therein (public authorities, higher education institutions and their associations, accreditation agencies and other institutions assessing the quality of higher education, the so-called stakeholders of higher education institutions) can be described and explained as decisions of players playing multiplayer and multilevel games for the organisation of education processes and for higher education. Games for education processes and for higher education are currently played not only in the hierarchical structure of the state, but also in a broader organisational perspective, which is the European Higher Education Area. Managing the quality of education in this area is not controlled top-down, and involves mainly arranging some binding and guiding institutional solutions which are to lead to an increased competitiveness of education processes and higher education offered by European higher education institutions.