On a Fundamental Property of Talman-Yang's Auction under Price Control

Recently Talman and Yang (2008) examined an assignment market under price control. In the market a number of heterogeneous items are to be sold to several bidders. Each bidder has a valuation on each item. The seller has a reservation price for every item. Meanwhile every item has a ceiling price imposed by a central planner. Due to price controls, there usually do not exist market-clearing prices. To deal with this allocation problem, Talman and Yang proposed a dynamic auction with rationing that always yields a constrained equilibrium. In this paper we establish that this dynamic auction can actually ï¬nd a core allocation in ï¬nite steps, resulting in a Pareto efficient outcome. A core allocation consists of an assignment of items and a supporting price vector for the assignment.