Xi Chen
ABSTRACT
We introduce the notion of non-monotone utilities, which covers a wide variety of utility functions in economic theory. We show that it is PPAD-hard to compute an approximate Arrow-Debreu market equilibrium in markets with linear and non-monotone utilities. Building on this result, we settle the long-standing open problem regarding the computation of an approximate Arrow-Debreu market equilibrium in markets with CES utilities, by proving that it is PPAD-complete when the Constant Elasticity of Substitution parameter, ρ, is any constant less than -1.
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Index Terms
- The complexity of non-monotone markets
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