Scientific publications

М.М. Луценко.

Поиск точки на отрезке с использованием нескольких промежутков

// Математическая Теория Игр и ее Приложения, т. 18, в. 3. 2026. C. 45-79

Mikhail M. Lutsenko. Searching a point on the unit segment using multiple intervals // Mathematical game theory and applications. Vol 18. No 3. 2026. Pp. 45-79

Keywords: zero-sum game, search game, non-cooperative game, partial sum of games, analytical solution of game

Games involving point search on a segment using several intervals of varying lengths are considered. Some applications of the games to radio interception problems, statistical and non-cooperative multi-player games are indicated. To solve the games, minimal segment covers are constructed, and a representation of the game as a partial sum of a set of games on the unit square is used. A theorem on the existence of optimal equalizing strategies and their decomposition into basic measures is proved. A method for constructing optimal equalizing strategies based on solving an integer linear programming problem is presented. Solutions of the examples are presented in analytical form.

Indexed at RSCI, RSCI (WS)

vol18_3_45_lutsenko.pdf (589 Kb, total downloads: 5)

Last modified: October 12, 2026