1. Introduction

It is known that the problem of finding an equilibrium in a linear exchange model can be reduced to the linear complementarity problem [1]. Proposed by the author in [2], a polyhedral complementarity approach is based on a fundamentally different idea that reflects more the character of economic equilibrium as a concordance the consumers' preferences with financial balances. In algorithmic aspect, it may be treated as a realization of the main idea of linear and quadratic programming. It has no analogues and makes it possible to obtain the finite algorithms not only for the general case of classical linear exchange model [3], but also for more complicate linear models, in which there are two sets of participants: consumers and firms producing goods [4] (more references one can find in [5]). The simplest algorithms are those for

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a model with fixed budgets, known more as Fisher's problem. The convex programming reduction of it, given by Eisenberg and Gale [6], is well known. This result has been used by many authors to study computational aspects of the problem. Some reviews of that can be found in [7]. The polyhedral complementarity approach gives an alternative reduction of the Fisher's problem to a convex program [2, 8]. Only the well-known elements of transportation problem algorithms are used in the procedures obtained by this way [9]. These simple procedures can be used for getting iterative methods for more complicate models [5, 10].

The mathematical fundamental base of the approach is a special class of piecewise constant multivalued mappings on the simplex in R<sup>n</sup>, which possesses some monotonicity property (decreasing mappings). The problem is to find a fixed point of the mapping. The mappings in the Fisher's model proved to be potential ones. This makes it possible to reduce a fixed point problem to two optimization problems which are in duality similarly to dual linear programming problems. The obtained algorithms are based on the ideas of suboptimization [11]. The mapping for the general exchange model is not potential. The proposed finite algorithm can be considered as an analogue of the Lemke's method for linear complementarity problem with positive principal minors of the restriction matrix (class P) [12].
