K. Vela Velupillai (Department of Economics/ASSRU, Trento)
Incomputability in Economic Theory

The origins of classical recursion theoretic and computational complexity theoretic formalisms in core areas of economic theory - game theory and rational choice theory - can be traced to the pioneering articles by Herbert Simon, Michael Rabin and Hilary Putnam, in the 1950s and early 1960s. From the outset, particularly in Rabin's work, the issues of unsolvability, incomputability and undecidability played crucial roles in the effectivized formalisation of problems in playable games, satisfiable choice sets and rational behaviour. At the frontiers of economic theory, these issues have now taken on some analytical and computational significance via considerations of the incomputability of game theoretic, welfare theoretic and general equilibrium characterizations of varieties of formally - non-constructively and non-effectively - demonstrated equilibria. In this paper, after a brief survey of the historical evolution of the subject of what I have come to call Computable Economics, an attempt is made to outline also the frontiers of the subject and identify directions for future research on incomputability and undecidabilty in economic theory.