Market Equilibria with Hybrid Linear-Leontief Utilities

We introduce a new family of utility functions for exchange markets. This family provides a natural and ”continuous” hybridization of the traditional linear and Leontief utilities and might be useful in understanding the complexity of computing and approximating of market equilibria. We show that a Fisher equilibrium of an exchange market with m commodities and n traders and hybrid linear-Leontief utilities can be found in O( √ mn(m+n)L) time. Because this family of utility function contains Leontief utility functions as special cases, finding an approximate Arrow-Debreu equilibria with hybrid linear-Leontief is PPAD-hard in general. In contrast, we show that, when the linear component is wellconditioned and the Leontief components are structured and finite, we can efficiently compute an approximate Arrow-Debreu equilibrium.