Game-theoretic applications of a relational risk model
This work provides a foundational framework for risk analysis in game theory, which could impact decision-making in fields like politics, but it appears incremental as it builds on existing mathematical structures.
The paper tackles the problem of modeling risk in game theory by introducing a relational risk theory based on partial orders and semilattices, and applies it to political decision-making to investigate solutions using optimality principles.
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.