Optimality versus practicality in market design: A comparison of two double auctions

We consider a market for indivisible items with m buyers and m sellers. Traders privately know their values/costs, which are statistically dependent. Two mechanisms are considered. The buyer's bid double auction collects bids and asks from traders and determines the allocation by selecting a market-clearing price. It fails to achieve all possible gains from trade because of strategic bidding. The designed mechanism is a revelation mechanism in which honest reporting of values/costs is incentive compatible and all gains from trade are achieved. This optimality, however, comes at the expense of plausibility: (i) the monetary transfers among the traders are defined in terms of the traders' beliefs about each other's value/cost; (ii) a trader may suffer a loss ex post; (iii) the mechanism may run a surplus/deficit ex post. We compare the virtues of the simple yet mildly inefficient buyer's bid double auction to the flawed yet perfectly efficient designed mechanism.