Game-theoretic applications of a relational risk model
  The report suggests the concept of risk, outlining two mathematical
structures necessary for risk genesis: the set of outcomes and, in a general
case, partial order of preference on it. It is shown that this minimum partial
order should constitute the structure of a semilattice. In some cases, there
should be a system of semilattices nested in a certain way. On this basis, the
classification of risk theory tasks is given in the context of specialization
of mathematical knowledge. In other words, we are talking about the development
of a new rela-tional risk theory. The problem of political decision making in
game-theoretic formulation in terms of having partial order of preference on
the set of outcomes for each par-ticipant of the game forming a certain system
of nested semilattices is consid-ered as an example of a relational risk
concept implementation. Solutions to the problem obtained through the use of
various optimality principles are investi-gated.
