An Informationally-Robust Market Model of Perfect Competition

A large number of buyers with single unit demand have a common value for a good being sold. Buyers decide whether or not they wish to purchase the good, available goods are rationed among those who wish to purchase, and the market price is a function of the number of buyers who wish to purchase. We characterize pricing rules for which, as the number of buyers grows large, the expected market price converges to the expected value, regardless of the buyers’ information and equilibrium strategies; these are pricing rules that have vanishing price impact and are asymptotically inelastic. Interpreting the pricing rule as a market supply function, we also prove that as long as the pricing rule has vanishing price impact, then in the large market, welfare is at least that which obtains if the buyers have no information about the value. We extend our results to the case where there is also an idiosyncratic component to the value.