On the Efficiency of Fair and Truthful Trade Mechanisms

We consider the impact of fairness requirements on the social efficiency of truthful mechanisms for trade, focusing on Bayesian bilateral-trade settings. Unlike the full information case in which all gains-from-trade can be realized and equally split between the two parties, in the private information setting, equitability has devastating welfare implications (even if only required to hold ex-ante). We thus search for an alternative fairness notion and suggest requiring the mechanism to be KS-fair: it must ex-ante equalize the fraction of the ideal utilities of the two traders. We show that there is always a KS-fair (simple) truthful mechanism with expected gains-from-trade that are half the optimum, but always ensuring any better fraction is impossible (even when the seller value is zero). We then restrict our attention to trade settings with a zero-value seller and a buyer with value distribution that is Regular or MHR, proving that much better fractions can be obtained under these conditions.