Mechanisms for Risk Averse Agents, Without Loss

Auctions in which agents ’ payoffs are random variables have received increased attention in recent years. In particular, recent work in algorithmic mechanism design has produced mech-anisms employing internal randomization, partly in response to limitations on deterministic mechanisms imposed by computational complexity. For many of these mechanisms, which are often referred to as truthful-in-expectation, incentive compatibility is contingent on the as-sumption that agents are risk-neutral. These mechanisms have been criticized on the grounds that this assumption is too strong, because “real ” agents are typically risk averse, and more-over their precise attitude towards risk is typically unknown a-priori. In response, researchers in algorithmic mechanism design have sought the design of universally-truthful mechanisms — mechanisms for which incentive-compatibility makes no assumptions regarding agents ’ attitudes towards risk. Starting with the observation that universal truthfulness is strictly stronger than incentive compatibility in the presence of risk aversion, we show that any truthful-in-expectation mecha-nism can be generically transformed into a mechanism that is incentive compatible even when agents are risk averse, without modifying the mechanism’s allocation rule. The transformed mechanism does not require reporting of agents ’ risk profiles. Equivalently, our result can be stated as follows: Every (randomized) allocation rule that is implementable in dominant strate-gies when players are risk neutral is also implementable when players are endowed with an arbitrary and unknown concave utility function for money. Our result has two main implications: (1) A mechanism designer concerned with an objective which depends only on the allocation rule of the mechanism can feel free to design a truthful-in-expectation mechanism, knowing that the risk-neutrality assumption can be removed by a generic black-box transformation. (2) Studying universally-truthful mechanisms under the pretense of robustness to risk aversion is no longer justified.