Jernej Čopič: Optimal robust bilateral trade: burning money

Abstract: We provide an example of a robust bilateral trading mechanism, which cannot be represented as a randomized posted price, contrary to the main theorem in Hagerty and Rogerson 1987, and which is not ex post Pareto dominated by any randomized posted price, contrary to the main theorem in Copic and Ponsati 2016. We identify a hidden assumption in these theorems: the payment by the seller equals the receipt of the buyer in all events when trade takes place. In the present example of  trading mechanism there is some money burning (disposal of money) in some trading events, i.e., the payment by the buyer is larger than the seller’s receipt. This demonstrates that in the absence of any external forces or frictions, two prices, one for the buyer and one for the seller (as in a bid-ask spread) are Pareto optimal under incentive and participation constraints due to the traders' private information.