Abstract
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.
Highlights
The model of general equilibrium by G
In the axiomatic-topological framework, the cumulative and innovative extensions of a production system were defined and their properties proved [2], including the economic mechanisms describing the evolution from an arbitrary economic system to its cumulative extension and evolution to its innovative extension [3]
We present the production system of a general equilibrium model described in the language of game theory
Summary
The model of general equilibrium by G. In the axiomatic-topological framework, the cumulative and innovative extensions of a production system were defined and their properties proved [2], including the economic mechanisms describing the evolution from an arbitrary economic system to its cumulative extension (price-preserving mechanism) and evolution to its innovative extension (qualitative mechanism) [3] It was proved [6] that acting optimally at each stage of the evolution in both those processes, the producers are able to reach an optimal state in the final system. In order to provide the answer for the question posed, first, we recall the concept of a parametric-multicriteria game and the result on lower semicontinuity of the parametric multicriteria-weak Nash equilibria, following [17] Formulation of this theorem requires Kuratowski convergence of suitable sequences of sets.
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