Informationally Robust Bilateral Trade

Abstract:  We propose a new class of mechanisms for bilateral trade: Buyer and seller both bid non-negative real numbers, the probability of trade is an increasing function of the sum of the bids, and the trading price is a weighted average of a high price and a low price, with weights proportional to the bids of buyer and seller, respectively. These mechanisms provide non-trivial guarantees for gains from trade, regardless of the distribution of values and the structure of information. We also construct information structures with binary values in which the mechanisms are optimal, thus showing that the guarantee is unimprovable. The key feature of the mechanisms is that they balance the "virtual gains from trade" across lots of action profiles. We also discuss an extended class of mechanisms in which the buyer (or seller) can unilaterally sell (or buy) back the good at a price that only depends on their own bid. These mechanisms provide better guarantees when the values are especially likely to be high or low, respectively.

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