Liquid markets and competition

A market is liquid if no individual's actions have a big effect on the prices of goods traded in that market. Perfectly competitive markets are therefore perfectly liquid. It is well known that market liquidity can be achieved by increasing the number of traders so that individual trades are small compared to total trades. We show that even when there are only few traders, market liquidity can be achieved through large short sales in which net trades are small relative to gross trades. In particular, for a natural variant of the market game which permits unlimited short sales, we show that there is always a Nash equilibrium allocation arbitrarily close to a competitive equilibrium allocation. Of course, not all NE are near competitive. Only the large-short-sales NE are nearly liquid and hence close to CE.