Market Equilibrium under Separable, Piecewise-Linear, Concave Utilities

We consider Fisher and Arrow-Debreu markets under additively-separable, piecewise-linear, concave utility functions, and obtain the following results: ? For both market models, if an equilibrium exists, there is one that is rational and can be written using polynomially many bits. ? There is no simple necessary and sufficient condition for the existence of an equilibrium: The problem of checking for existence of an equilibrium is NP-complete for both market models; the same holds for existence of an -approximate equilibrium, for = O(n-5 ). ? Under standard (mild) sufficient conditions, the problem of finding an exact equilibrium is in PPAD for both market models. ? Finally, building on the techniques of [CDDT09] we prove that under these sufficient conditions, finding an equilibrium for Fisher markets is PPAD-hard.

• Type: Conference
• Year: 2010
• Where: ICS
• Authors: Vijay V. Vazirani, Mihalis Yannakakis
• Keywords: ICS 2010, Theoritical Computer Science