Exchange Market Equilibria with Leontief ’s Utility: Freedom of Pricing Leads to Rationality

(Paper by Yinyu Ye http://www.optimization-online.org/DB_FILE/2006/08/1445.pdf)

This paper studies the equilibrium property and algorithmic complexity of the
exchange market equilibrium problem with concave piece-wise linear functions, which include linear and Leontief ’s utility functions as special cases. We show that the Fisher model again reduces to the weighted analytic center problem, and the same
linear programming complexity bound applies to computing its equilibrium. However, the story for the Arrow-Debreu model with Leontief ’s utility becomes quite different. We show that, for the first time, solving this class of Leontief exchange economies is equivalent to solving a linear complementarity problem whose algorithmic complexity is finite but not polynomially bounded.