This paper establishes a lower bound on the computational complexity of smooth functions between smooth manifolds. It generalizes one for finite (Boolean) functions obtained (by Arbib and Spira [2]) by counting variables. Instead of a counting procedure, which cannot be used in the infinite...

This paper establishes a lower bound on the computational complexity of smooth functions between smooth manifolds. It generalizes one for finite (Boolean) functions obtained (by Arbib and Spira [2]) by counting variables. Instead of a counting procedure, which cannot be used in the infinite...

This paper obtains finite counterparts of previous results that showed the informational efficiency of the Walrasian mechanism among all mechanisms yielding Pareto-optimal individually rational trades in exchange economies while using a continuum of possible messages. In particular, we develop...

This paper obtains finite analogues to propositions that a previous literature obtained about the informational efficiency of mechanisms whose possible messages form a continuum. Upon reaching an equilibrium message, to which all persons “agree”, a mechanism obtains an action appropriate to...

In this paper we consider the situation of an investor facing uncertainty, and whose objective is to survive. First we characterize the probability of survival of a passive agent who does not attempt to influence the evolution of the environment. Secondly, we look at an active agent who chooses...