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The Complexity of Non-Monotone Markets

We introduce the notion of non-monotone utilities, which covers a wide variety of utility functions in economic theory. We then prove 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 utility functions, by proving that it is PPAD-complete when the Constant Elasticity of Substitution parameter ρis any constant less than -1.

preprint2012arXivOpen access
Xi ChenDimitris PaparasMihalis Yannakakis
Computer Science and Game TheoryComputational Complexity
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Xi ChenDimitris PaparasMihalis Yannakakis

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