DYNAMIC MATRIX GAMES AND THEIR MIXED EXTENSION

Abstract

A new class of game models, called dynamic matrix games (DMG) was introduced in [2] as a generalization of the classical matrix games considering the time factor. Such a generalization seems natural both from the theoretical point of view, the dynamic zero-sum games once being constructed by adding dynamics in the infinite zero-sum games, and from the practical point of view – as the expansion of application field of the matrix games theory. The model of the DMG was constructed in [2], the basic concepts were defined, the class of admissible pure strategies was introduced and the using of minimax principle was substantiated.The concept of mixed combinated strategies is introduced in this paper; the questions of the necessary and sufficient optimality signs, the existence of optimal strategies and their dynamic stability are investigated in this class of strategies.

Keywords

• matrix games
• mixed k-strategies
• optimal trajectory
• dynamic stability