Can Producers’ Price War End Up in an Optimal Allocation?

The paper presents a theoretical framework for the phenomenon of the price war in the context of general equilibrium, with special attention to the production system. The natural question that arises is whether Nash-optimal production plans being the reactions to the changing prices can finally approximate a Nash-optimal production plan at the end of this war. To provide an answer, the production system is described as a parametric-multicriteria game. Referring to some results on the lower semicontinuty of the parametric weak-multicriteria Nash equilibria, we provide a positive answer for the stated problem.

SELECTED ASPECTS OF MODELING THE PROCESS OF EVALUATING BUSINESS STRATEGIES FOR SUSTAINABLE ECONOMIC DEVELOPMENT OF IRON ORE ENTERPRISES

The theoretical principles of modeling the process of evaluation of business strategies for ensuring sustainable economic development of iron ore enterprises are considered in the article, taking into account the current state of the domestic economy. The basic model of the situation of making a rational decision concerning the problem of optimization of business strategies in the conditions of uncertainty and conflict of the market environment is defined, which is a generalized matrix of the problem of mathematical programming, the solution of which is the optimal parameters of a mixed strategy for managing the sustainable development of iron ore enterprise. The procedure of multicriteria game-theoretic evaluation of alternatives in the application of mathematical theory of conflict situations in the work is recommended to be carried out according to a certain algorithm, which reflects the sequence of stages of modeling the effective evaluations of individual business strategies when using the functionals of evaluation with negative, but continuous. In the work it is proved that not only research of their optimality but also issues related to forecasting a guaranteed positive positive result is of particular importance when forming situations of financial and economic substantiation and making management decisions regarding individual business strategies of the enterprise. As a result of using the proposed methodological approaches, this study achieves a scientifically sound isolation of certain key business processes of the enterprise's production and economic system in order to carry out more in-depth analysis of problematic business operations and to make adequate strategic decisions regarding the prospects of sustainable economic development of the iron ore enterprises.

Multiobjective Games for Detecting Abnormally Expressed Genes

A class of multiobjective games with applications to a medicine setting is studied. We consider the vector Shapley value and the vector Banzhaf value for a multicriteria game and we apply them to a microarray game. We give an axiomatic characterization too.

A REFINEMENT CONCEPT FOR EQUILIBRIA IN MULTICRITERIA GAMES VIA STABLE SCALARIZATIONS

In a finite multicriteria game, one or more systems of weights might be implicitly used by the agents by playing a Nash equilibrium of the corresponding trade-off scalar games. In this paper, we present a refinement concept for equilibria in finite multicriteria games, called scalarization-stable equilibrium, that selects equilibria stable with respect to perturbations on the scalarization. An existence theorem is provided together with some illustrative examples and connections with some other refinement concepts are investigated.