Consider the revenue maximization problem of a risk-neutral seller with m heterogeneous items for sale to a single additive buyer, whose values for the items are drawn from known distributions. If the buyer is also risk-neutral, it is known that a simple and natural mechanism, namely the better of selling separately or pricing only the grand bundle, gives a constant-factor approximation to the optimal revenue. In this paper we study revenue maximization without risk-neutral buyers. Specifically, we adopt cumulative prospect theory, a well established generalization of expected utility theory. Our starting observation is that such preferences give rise to a very rich space of mechanisms, allowing the seller to extract arbitrary revenue. Specifically, a seller can construct extreme lotteries that look attractive to a mildly optimistic buyer, but have arbitrarily negative true expectation. Therefore, giving the seller absolute freedom over the design space results in absurd conclusions; competing with the optimal mechanism is hopeless. Instead, in this paper we study four broad classes of mechanisms, each characterized by a distinct use of randomness. Our goal is twofold: to explore the power of randomness when the buyer is not risk-neutral, and to design simple and attitude-agnostic mechanisms—mechanisms that do not depend on details of the buyer’s risk attitude—which are good approximations of the optimal in-class mechanism, tailored to a specific risk attitude. Our main result is that the same simple and risk-agnostic mechanism (the better of selling separately or pricing only the grand bundle) is a good approximation to the optimal non-agnostic mechanism within three of the mechanism classes we study.

考虑具有m的风险中性卖方的收益最大化问题出售给单个附加购买者的异类物品，其物品的价值来自已知的分布。如果买方也是风险中性的，那么众所周知，一个简单而自然的机制，即最好是单独销售还是只对大捆绑定价，会给出最优收入的常数因子近似值。在本文中，我们研究了没有风险中性买家的收入最大化。具体来说，我们采用累积前景理论，这是预期效用理论的一个完善的概括。我们的初步观察是，这种偏好产生了非常丰富的机制空间，允许卖家获取任意收入。具体来说，卖家可以构建极端的彩票，看起来对温和乐观的买家有吸引力，但具有任意负面的真实期望。所以，给卖方对设计空间的绝对自由会导致荒谬的结论；与最优机制竞争是无望的。相反，在本文中，我们研究了四大类机制，每种机制的特点是对随机性的不同使用。我们的目标是双重的：在买方不是风险中立的情况下探索随机性的力量，以及设计简单且与态度无关的机制——不依赖于买方风险态度细节的机制——这是最优的近似值班级机制，针对特定的风险态度量身定制。我们的主要结果是，在我们研究的三个机制类别中，相同的简单且与风险无关的机制（单独销售或仅对大捆绑定价更好）是对最佳非不可知机制的良好近似。