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- Title
Risk-Robust Mechanism Design for a Prospect-Theoretic Buyer.
- Authors
Liu, Siqi; Miller, J. Benjamin; Psomas, Alexandros
- Abstract
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.
- Subjects
PROSPECT theory; UTILITY theory; EXPECTED utility; LOTTERIES
- Publication
Theory of Computing Systems, 2022, Vol 66, Issue 3, p616
- ISSN
1432-4350
- Publication type
Article
- DOI
10.1007/s00224-021-10054-9