Survey of some results in choice theory

Abstract

The independent project will focus on the problem of resource allocation across different sectors.The sectors in question could be divisions in a company, states in a country, sectors in an economy, etc.Each of these sectors in question has a yield associated with it.Thus the purpose is to allocate investment among these sectors, so as to obtain an acceptable vector of yields. Now there can be several rules for picking vectors from the feasible set of yield vectors.Our purpose here is to see under what conditions; a choice function is representable by a utility function.In this regard, in the first part, a no. of results have been demonstrated in the I- dimensional case.In the last part, some important results in the 2- dimensional case have been covered.