Market equilibrium via a primal--dual algorithm for a convex program
Journal of the ACM (JACM)
Continuity Properties of Equilibria in Some Fisher and Arrow-Debreu Market Models
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
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Continuity of the mapping from initial endowments and utilities to equilibria is an essential property for a desirable model of an economy - without continuity, small errors in the observation of parameters of the economy may lead to entirely different predicted equilibria. We show that for the linear case of Fisher's market model, the (unique) vector of equilibrium prices, p = p(m, U) is a continuous function of the initial amounts of money held by the agents, m, and their utility functions, U. Furthermore, the correspondence X(m, U), giving the set of equilibrium allocations for any specified m and U, is upper hemicontinuous, but not lower hemicontinuous. However, for a fixed U, this correspondence is lower hemicontinuous in m.