Informatica

When handling engineering problems associated with optimal alternative selection a researcher often deals with not sufficiently accurate data. The alternatives are usually assessed by applying several different criteria. A method takes advantage of the relationship between fuzzy sets and matrix game theories can be offered for multicriteria decision-making. Practical investigations have already been discussed for selecting the variants water supply systems.

The objective of this paper is the description, justification, and web-based implementation of polynomial time algorithms for equilibrium search of Quadratic Bimatrix Games (QBG). An algorithm is proposed combining exact and heuristic parts. The exact part has the Irelevant Fraud (IF) component for cases when an equilibrium exists with no pure strategies. The Direct Search (DS) component finds a solution if an equilibrium exists in pure strategies. The heuristic Quadratic Strategy Elimination (QSE) part applies IF and DS to reduced matrices obtained by sequential elimination of strategies that lead to non-positive IF solutions. Finally, penalties needed to prevent unauthorized deals are calculated based on Nash axioms of two-person bargaining theory. In the numeric experiments QSE provided correct solution in all examples. The novel results include necessary and sufficient conditions when the QBG problem is solved by IF algorithm, the development of software and the experimental testing of large scale QBG problems up to n=800. The web-site http://pilis.if.ktu.lt/~jmockus includes this and accompanying optimization models.

This paper considers the main positions of one‐sided and two‐sided problems. For one‐sided problems only the method of solution “the distance to the ideal point” is discussed in the actual version. For two‐sided problems a distinction is made between games with rational behaviour and games against nature. The main strategic principles are as follows: simple min‐max principle, extended min‐max principle, Wald's rule, Savage criterion, Hurwicz's rule, Laplace's rule, Bayes's rule, Hodges‐Lehmann rule. Questions of transforming the decision‐making matrix are considered. The article gives the description of a software as well as an example of an investment variant estimation.

Two examples of open-loop differential games are considered in the paper. Starting with simplified dynamic Duel, further it was developed to differential economic Duel modelling problem.

A concept of regional technological cooperation is developed based on a cooperative game theoretic model, in which a plan of payoff distributions induces an agreement that is acceptable to each participant. Under certain conditions, the underlying game is shown to be convex, and hence to have a nonempty core with the Shapley value allocations belonging to the core. A compensation scheme is devised based on the Shapley value allocations, whereby participants who enjoy a greater payoff with respect to the technological cooperation compensate the participants who receive a relatively lesser payoff via cooperation. In this manner, regional technological cooperation can bring overall benefits to all the involved players in the game. Some insightful examples are provided to illustrate the methodological concept.