[1] In 1954 she entered the Mathematics and Mechanics Faculty of Leningrad State University, receiving her kandidat degree in 1963 under the supervision of Nikolai Vorobyov.
She defended her doktor nauk degree in 1984 at the Faculty of Computational Mathematics and Cybernetics, Moscow State University.
The most famous result of Bondareva, obtained during her PhD studies, is the necessary and sufficient conditions for the core of a cooperative game with transferable utility to be non-empty.
It was published in the collection "Problems of Cybernetics", quite a prestigious publication, but not translated into English, and was not noticed in the West.
Having learned about the publication of Bondareva, Shapley unconditionally recognized its priority, which ensured its universal recognition.
Throughout the 1970s and 1980s, Bondareva studied game-theoretic dominance properties expressed in terms of abstract binary relations, essentially following the example of the seminal monograph Neumann and Morgenstern.
In the late 1970s, Bondareva, together with her students T. E. Kulakovskaya and N. I. Naumova, brainstormed the problem of the existence of a von Neumann-Morgenstern solution in cooperative games with transferable utility (the possibility of non-existence was already known by that time ).