We provide a "computable counterexample" to the Arrow-Debreu competitive equilibrium existence theorem [2]. 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...

We present a theoretical view of computation, delineating what types of approximations are possible and what types are impossible. A practical consequence is an approximation algorithm with numerous applications. For several classical problems (finding maximizers, fixed points, equilibrium...

A natural bound on rationality arises from computability:-I can't use a number if I can't compute it, and \hfill\break -I can't use a preference relation or utility function that I can't compute.We assume that all magnitudes (quantities, prices) are computable real numbers, and all relations and...