Withholding and damage in Bayesian trade mechanisms

Abstract

We study the optimality of allowing the designer to withhold or damage resources in Bayesian incentive compatible mechanisms for bilateral trade with independent private values. The following results hold when the buyer and the seller have discrete value distributions. Burning money or withholding the good from both traders never enhances welfare. Similarly, damaging the good for the buyer cannot increase welfare. By contrast, damaging the good for the seller may improve welfare. However, such welfare improvements are possible only if the damage hurts some lower valuation type of seller more severely than the highest valuation type. Results extend to the case of continuous value distributions under certain hypotheses regarding virtual values. Methods also apply to optimal Bayesian implementation for allocation problems. In the absence of property rights, damaging goods for any agent has negative welfare consequences.