# Vorob’ev, Nikolai N. (1925–1995)

**DOI:**https://doi.org/10.1057/978-1-349-95189-5_2536

## Abstract

Nikolay Vorob’ev is commonly regarded as the founder and the leader of game-theoretic school in the former Soviet Union.

### Keywords

Coalitional games Game theory Markov, A. Morgenstern, O. Probability theory Von Neumann, J. Vorob’ev, NNikolay Vorob’ev is commonly regarded as the founder and the leader of game-theoretic school in the former Soviet Union.

Vorob’ev was born on 18 September 1925 in Leningrad (now St Petersburg). His father was a lawyer and his mother a surgeon. Beginning his education at technical institutes in Izevsk and Moscow, he returned to Leningrad in 1944 and become a student at the Leningrad Shipbuilding Institute. In 1946 he began study at the Faculty of Mathematics and Mechanics of the Leningrad State University. In 1948 he left the Shipbuilding Institute and graduated from the university. In 1947 Vorob’ev published his first paper in semigroup theory.

In 1948 Vorob’ev started a postgraduate programme at the Leningrad branch of the Steklov Mathematical Institute. His supervisor was Professor A.A. Markov, under whose influence he studied constructive mathematical logic, which was rapidly developing at that time. His Candidate of Science thesis in mathematics was devoted to logical deduction rules in systems with strong negation. He received his Candidate of Science degree in 1952. In the same year he joined the Steklov Mathematical Institute as a junior research associate. Here he once more changed his scientific interests and started research concerned with both algebra and probability theory.

Axiomatic training in algebra and logic, along with studies in probability theory, permitted Vorobe’ev to make a transition to the study of game theory. His paper ‘Controlled Processes and Game Theory’ (1955) was the first paper in game theory published in the former Soviet Union. His 1959 review article ‘Finite Noncooperative Games’ served for many years as a primary Russian language source for understanding game theory. In the next five years Vorob’ev made an attempt to develop the theory of coalitional games, that is, games in which players belonging to one coalition are acting as one player, and therefore mixed strategies have to be defined as correlated families of measures. To prove the existence of stable outcomes in such games, he solved some non-standard problems from combinatorial topology and probability theory, thus combining ideas and methods from various branches of mathematics. At that time he also made interesting generalizations of H. Kuhn’s equivalence theorem about behaviour strategies in extensive games with perfect recall, proposed an algorithm on enumerating equilibrium points in bimatrix games and studied games with forbidden situations. These results constituted the basis of his Doctor of Science thesis, which he defended in 1961. In the same year he organized the Soviet Union’s first laboratory for game theory and operations research at the Steklov Mathematical Institute of the Academy of Sciences. Under his supervision more than 30 students obtained candidate and doctoral degrees in game theory. In 1968 Vorob’ev organized the first all-Union game theory conference in Erevan (Armenia) and the second in 1971 in Vilnius (Lithuania). He was the main speaker at both conferences, which each attracted more than 100 participants. His addresses focused on methodological and philosophical aspects of game theory as well as areas of applications. He forecast the application of game theory in economics, military affairs, biology, law, ethics, sociology, medicine and literature.

In 1975 his laboratory moved to the Institute for Socio-Economic Problems. Unfortunately, the administration of the institute considered any application of mathematical methods in social sciences as inconsistent with prevailing Marxist-Leninist dogmas. Game theory was no exception, which was why the laboratory was forced to concentrate on mathematical problems arising in game theory. Vorob’ev wrote an interesting monograph *Foundations of Game Theory: Noncooperative Games* (published in English translation in 1994) and considered it the first volume in a planned series of books on game theory. The second volume, ‘Cooperative Games’ was not completed. He also wanted to write a volume titled ‘Dynamic Games’.

Vorob’ev was a brilliant lecturer. He taught part-time at the Leningrad State University and many other universities in Russia and elsewhere, delivering courses in game theory, algebra, probability theory and number theory. He wrote many textbooks, the most popular among which is *Game Theory for Economists and System Scientists* (published in English translation in 1977). He edited most of the translations of the principal Western scientific monographs into Russian, including the famous *Theory of Games and Economic Behavior* by J. von Neumann and O. Morgenstern (1944). He also edited two bibliographic indices on game theory literature up to 1974. They contain about 5,000 summaries of game-theory books and papers from all over the world.

## See Also

## Selected Works

1955. Controlled processes and game theory. *Viestnik of Leningrad University* 4(11):49.

1958. Equilibrium points in bi-matrix games. *Theory of Probability and its Applications* 3:297–309.

1959. Finite non-cooperative games. *Russian Mathematical Surveys* 14(4):21–56.

1960. About partitioned strategies. *Probability Theory and Applications* 5:457–9.

1970. The present state of the theory of games. *Russian Mathematical Surveys* 25(2):77–36.

1976. *Game theory: Bibliographic index*. Leningrad: Nauka.

1977. *Game theory for economists and system scientists*. New York: Springer.

1980. *Game theory: Bibliographic index*. Leningrad: Nauka.

1994. *Foundations of game theory: Noncooperative games*. Boston: Birkhauser.

### Bibliography

- von Neumann, J., and O. Morgenstern. 1944.
*Theory of games and economic behavior*. Princeton: Princeton University Press.Google Scholar