Efficient Mechanisms with Risky Participation
There is a fundamental incompatibility between efficiency, interim individual rationality, and budget-balance in mechanism design, even for extremely simple settings. Yet it is possible to specify efficient mechanisms that satisfy participation and budget-balance constraints in expectation, prior to types being realized. We do so here, in fact deriving mechanisms that are individually rational for each agent even ex post of other agents' type realizations. However, participation must still bear some risk of loss. For agents that are risk neutral, we show how the center can extract the entire surplus in expectation, or alternatively provide an equal expected share of the surplus for each participant, without violating dominant strategy incentive compatibility, efficiency, or ex ante budget-balance. We compare these solutions to a third efficient mechanism we design explicitly to address risk aversion in trade settings: payments are defined to minimize the odds of loss, satisfying ex ante participation constraints for agents with attitudes toward risk ranging from neutrality to high loss-aversion.