An iterative approach for searching an equilibrium in piecewise linear exchange model

Abstract

The exchange model with piecewise linear separable concave utility functions is considered. This consideration extends the author’s original approach to the equilibrium problem in a linear exchange model and its variations. The conceptual base of this approach is the scheme of polyhedral complementarity. It has no analogs and made it possible to obtain the finite algorithms for some variations of the exchange model. Especially simple algorithms arise for linear exchange model with fixed budgets (Fisher’s model). This is due to monotonicity property inherent in the models and potentiality of arising mappings. The algorithms can be considered as a procedure similar to the simplex-method of linear programming. It is natural to study applicability of the approach for more general models. The considered piecewise linear version of the model reduces to a special exchange model with upper bounds on variables and the modified conditions of the goods’ balances. For such a model the monotonicity property is violated. But it remains, if upper bounds are substituted by financial limits on purchases. This is the idea of proposed iterative algorithm for initial problem. It is a generalization of an analogue for linear exchange model.