Clearing Markets with Indivisible Supply and Demand

We show that the problem of clearing markets using a continuous call auction with indivisible demand and supply requires solving hard computational problems such as the generalized assignment problem and the bin packing problem. This is in stark contrast to the case where the demand and supply is continuous and market clearing is computationally straightforward. We examine the structure of the market clearing problem for the two institu-tions - the continuous call auction and the continuous double auction. The indi-visible nature of the supply and demand introduces waste in allocating supply to demand an d hence moves the equilibrium away from the point where the supply and demand curves intersect. An alternate formulation for assigning demand to
supply that maximizes net revealed surplus is introduced. Several research issues pertaining to the allocation of the net revealed surplus to buyers and sellers are identified. Additionally, we show that the institution of a. continuous double auction is in fact an approximation of the continuous call auction where a greedy approach is used to allocate supply to demand in real time as bids and asks arrive. The approach used in a continuous double auction can be viewed as an online algorithm for solving the generalized assignment problem. Several theoretical and simulation based research issues are identified to characterize the efficiency of the continuous double auction.