On one correctness problem for minimax

M. S. Nikol'skii

Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 33 (2023) no. 2, pp. 275-280

Résumé

In game theory and operations research theory, a minimax often appears for a function $f(x,y)$ that depends on two vector variables $x$, $y$. Many works have been devoted to the study of the properties of minimax (or maximin). A minimax can be interpreted as the smallest guaranteed result for the minimizing player (the minimizing operator). In the study of minimax problems, various correctness issues are of some interest. This paper is devoted to one of these issues. In it, vectors $x$, $y$ belong to compacts $P$, $Q$ of corresponding Euclidean spaces $R^k$, $R^l$, and function $f(x,y)$ is continuous on product of spaces $R^k\times R^l$. The paper considers the dependence of minimax on small changes of compacts $P$, $Q$ in the Hausdorff metric. The continuity of the dependence of minimax on small variations of compacts $P$, $Q$ is proved.

Détail

Keywords: game theory, operations research, minimax, Hausdorff metric, correctness.