Self-Covariant Solutions To Cooperative Games With Transferable Utilities
Two-person games and cost/surplus sharing problems are worth for studying because they are the base for their extending to the classes of such problems with variable population with the help of very powerful consistency properties. In the paper a family of cost-sharing methods for cost sharing problems with two agents is extended to a class of solutions for two-person cooperative games that are larger than both cost-sharing and surplus-sharing problems, since cooperative games have no restrictions on positivity of costs and surpluses. The tool of the extension is a new invariance axiom - self covariance - that can be applied both to cost-sharing methods and to cooperative game solutions. In particular, this axiom replaces the Lower composition axiom which is not applicable to methods for profit sharing problems.
The test assignments are given to the main topics of the textbook Probability theory and mathematical statistics for engineering and technical areas (Moscow, 2017, Yurayt ed.) In two parts: tests - tasks and tests - theoretical exam questions. The tests of each part are presented in two forms: complete (with solutions and answers) and - for working with students (without solutions and answers) with four possible answers in each test.