The paper examines the new modes of functioning of the institutes of the Russian Academy of Sciences, using tools of the economy of science, the theories of the firm and the game theory. A three-fold typology for these organizations is proposed. Game models for each type are constructed. A special attention is paid to the comparison of the efficiency of different modes of functioning, using different criteria. We argue that none of these types is optimal in all circumstances; each of these types can be the best choice for a given institute.