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The goal of this article is to demonstrate how mutually inter-related the two directions taken by the expansion and perfection of the game theory apparatus are, on one hand in the examination of redistribution systems and on the other hand in the analysis of contextual games. And to take advantage of this opportunity to present the latest findings attained in both areas and at the same time to characterize one of the most important types of the objects that our team has come across in the execution of the program as defined above – structures based on the mutual covering-up of the breaching of rules and generally accepted principles. These are objects without the theoretical grasp of which it is not possible to adequately describe the essence and social contexts of corruption and similar phenomena. And therein lies the social relevance and the originality of the topic. From the perspective of the development of science, the mentioned approach makes it possible, among other things, to explain some apparent discrepancies between game theory and this theory inspired by experiments.