Mathematical model of the network equilibrium for the case of competition in the conditions of incomplete awareness

DOI №______

Abstract

In this paper a network equilibrium framework for the modeling and analysis of competitive firms engaged in Internet advertising among multiple websites was developed. The optimization problem is formulated in relation to the quantitative, qualitative and temporal characteristics that arises before the decision maker (ODA) and implements the choice of alternatives, based on the evaluation of a set of goals that are often incompatible and contradictory. A scheme of equilibrium of the network was developed for modeling and analysis of the behavior of competing firms that advertise on many websites. A precise algorithm for the variational inequality of a special form is presented, which allows us to determine the equilibrium budget and the explicit expenses of advertising and shows that the solution of variational inequality satisfies the main equilibrium conditions for the model under consideration. The computation scheme in which the structure of the abstract network, which forms the basis of this task, is used. A numerical example is given.

Keywords: limit response, maximization of response, optimal Cune-Tucker conditions, Nash equilibrium

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