Optimality versus Practicality in Market Design: A comparison of Two Double Auctions

We consider a market for an indivisible good with m buyers, each of whom wishes to buy at most one item, and m sellers, each of whom has one item to sell. The traders privately know their values/costs, which are statistically dependent. Two mechanisms for trading are considered. The buyer's bid double auction collects bids and offers from traders and determines trade by selecting a market-clearing price. It fails to achieve all possible gains from trading because of the strategic bidding by traders. The designed mechanism is a revelation mechanism in which honest reporting of values/costs is incentive compatible and all gains from trading are achieved in equilibrium. 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 subsidy/deficit ex post, and (iv) the mechanism may be gamed by sellers. We compare here the virtues of the simple yet mildly inefficient buyer's bid double auction to the flawed yet perfectly efficient designed mechanism.