Several remarks on the role of certain positional and social games in the creation of the selected statistical and economic applications

The game theory was created on the basis of social as well as gambling games, such as chess, poker, baccarat, hex, or one-armed bandit. The aforementioned games lay solid foundations for analogous mathematical models (e.g., hex), artificial intelligence algorithms (hex), theoretical analysis of computational complexity attributable to various numerical problems (baccarat), as well as illustration of several economic dilemmas - particularly in the case where the winner takes everything (e.g., noughts and crosses). A certain gambling games, such as a horse racing, may be successfully applied to verify a wide spectrum of market mechanism, for example, market effectiveness or customer behavior in light of incoming information regarding a specific product. One of a lot applications of the slot machine (one-armed bandit) is asymptotically efficient allocation rule, which was assigned by T.L. Lai and H. Robbins (1985). In the next years, the rule was developed by another and was named a multi-armed. The aim of the paper is to discuss these social games along with their potential mathematical models, which are governed by the rules predominantly applicable to the social and natural sciences.