Abstract:
In the present paper, a model of market equilibrium with price
groups in the form of variational inequality for a single-product
market of an infinitely divisible product has been considered.
Unlike the classical model, in which all market participants are
equal and a single equilibrium price is found, it is assumed in this
paper that each seller or buyer can split the set of his/her
counterparties into non-overlapping groups and assign a certain
price function to each group. For this model, the equilibrium
conditions have been formulated and proved. The conditions for the
existence of a solution to the problem, based on the coercivity
property, have been also proposed and justified. For the model of market equilibrium with price groups, in which the
price functions of each seller/buyer for each group depend only on
the volume of purchases/sales of this seller/buyer in this group, a
method of coordinate descent for finding equilibrium states has been
proposed and its convergence has been proved. A series of test
calculations have been carried out for problems of different
dimension, a comparison of the coordinate descent method with
the gradient projection method has been performed, which
confirms the efficiency of the proposed method and its promising for
further investigation.
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