Non-computability of competitive equilibrium
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We provide a “computable counterexample” to the Arrow-Debreu competitive equilibrium existence theorem . In particular, we find an exchange economy in which all components are (Turing) computable, but in which no competitive equilibrium is computable. This result can be interpreted as an impossibility result in both computability-bounded rationality (cf. Binmore , Richter and Wong ) and computational economics (cf. Scarf ). To prove the theorem, we establish a “computable counterexample” to Brouwer's Fixed Point Theorem (similar to Orevkov ) and a computable analogue of a characterization of excess demand functions (cf. Mas-Colell , Geanakoplos , Wong ).
- Non-computability of competitive equilibrium
Volume 14, Issue 1 , pp 1-27
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- Key words and Phrases: Bounded rationality, Computability, General equilibrium, Recursive analysis.
- JEL Classification Numbers: D51, C68.
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