Recursive K-index and iterative H-index

An aggregated recursive K-index (Kazakhstan Science Index) is proposed as the new scientometric indicator and the “Kazakhstan Science Citation Index”.In particular, it is proposed to switch from a pure strategy for assessing the quality and effectiveness of R&D using the H-index (Hirsch index) to a mixed strategy (in the context of publication activity as a combination of cooperative and noncooperative games) using the K-index on subnational and H-index on international or differentiated levels. In the context of a hybrid strategy of the scientist's payoff functions. This transition is correct and in demand for a number of national scientific systems with limited financial, material, infrastructural and linguistic (in terms of the English language) potential. Scientific systems with highly developed indigenous (autochthonous) characteristics are also needed in some scientific areas.Some results on the counterproductivity of the Hirsch index for the Kazakh scientific system are presented. In particular, a significant increase in the H-index of Kazakh scientists was noted as the degree of scientific localization (national participation) decreased and as the degree of “foreign content” in science-intensive content increased within the framework of international joint collaboration. The ability of the delocalization of local scientific content in joint publications to increase the H-index of Kazakh scientists was discovered. This effect is interpreted and confirmed by the positive and negative correlation coefficients between the Hirsch indices and the form and degree of participation (role functions) of Kazakh scientists in joint publications.