Some Equivalence heoreni2

It is of interest to know whether results achieved through a process of " group rationality" could also have been achieved by maximization of " self-interest" at suitably chosen prices. One precise formulation of these intuitive notions is the proposition as to whether " allocations in the core are competitive equilibria ". This proposition dates back to Edgeworth and is false for an exchange economy with a finite number of agents. The question then arises as to whether core allocations are " similar " to competitive equilibriacan they be "'priced out" in some approximate sense? This paper presents ways of formalizing this " similarity ". The results are presented in the next section and an economic interpretation is given. This is followed by relating these results to other work on this problem. The last two sections are devoted to proofs of the theorems.