Bounded Rationalities and Computable Economies

Abstract

This paper studies economic equilibrium theory with a "uniformity principle" constraining the magnitudes (prices, quantities, etc.) and the operations (to perceive, evaluate, choose, communicate, etc.) that agents can use. For the special case of computability constraints, all prices, quantities, preference relations, utility functions, demand functions, etc. are required to be computable by finite algorithms. Then we obtain sharper versions of several traditional assertions on utility representation, existence of consumer demand functions, the fundamental welfare theorems, characterizations of market excess demands, and others. These positive results hold despite the fact that commodity and price spaces are no longer topologically complete. On the other hand, we give "computable counterexamples" to several traditional assertions, including the existence of a competitive equilibrium. The results can be interpreted as possibility and impossibility results in both computability-bounded rationality and in computational economics.