The Axiom of Determinacy and the Foundations of Economic Theory

TOHMÉ, FERNANDO

Bonn, Alemania

Congreso; Foundations of the Formal Sciences V; 2004

Rheinische Friedrich-Wilhelms-Universität Bonn

Many authors have pointed out serious shortcomings in the formalism of contemporary economic theory. In this brief paper we present a way to overcome some of them without losing the intuitions accepted by most economists. We will begin by showing that the computability of choice functions as well as the existence of economic equilibria may not be ensured in general if the assumed set theory is ZFC. We claim that a switch to an alternative set theory may help to get rid of some of these negative results. While this procedure seems a facile form to solve analytical problems, we think that it may have a legitimate importance for economic theory. In fact, alternative set-theoretical frameworks convey different intuitions about how agents behave when solving problems. One of these intuitions is that agents are able to play an infinite game of internal deliberation, for which they always have a winning strategy. An appropriate axiomatization of this idea is by means the Axiom of Determinacy (AD). Since this axiom is incompatible with other set theoretic postulates (in particular the Axiom of Choice, AC) we need to give an entire axiomatic structure for our reformed economic theory. We postulate that ZF +AD+ DC is the adequate set-theoretical universe for economic theory, where DC is the axiom of Dependent Choices.