2015/01/01 by Shant Boodaghians, Adrian Vetta · 4 citations
Business, Management and Accounting · Computer Science · Decision Sciences · Economics, Econometrics and Finance · Mathematics · #Auction Theory and Applications #Bidding #Combinatorial auction #Common value auction #Computer science #Consumer Market Behavior and Pricing #Economics #Finance #Function (biology) #Game Theory and Voting Systems #Mathematical economics #Mathematical optimization #Mathematics #Mechanism design #Microeconomics #Rationality #Valuation (finance) #cs.GT
paper · pdf · doi:10.1007/978-3-662-48433-3_10
published in Lecture notes in computer science, 125-136 (Springer Science+Business Media)
openalex publication_date 2015/01/01 · arxiv created 2015/07/27 · arxiv updated 2015/10/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Revealed preference techniques are used to test whether a data set is compatible with rational behaviour. They are also incorporated as constraints in mechanism design to encourage truthful behaviour in applications such as combinatorial auctions. In the auction setting, we present an efficient combinatorial algorithm to find a virtual valuation function with the optimal (additive) rationality guarantee. Moreover, we show that there exists such a valuation function that both is individually rational and is minimum (that is, it is component-wise dominated by any other individually rational, virtual valuation function that approximately fits the data). Similarly, given upper bound constraints on the valuation function, we show how to fit the maximum virtual valuation function with the optimal additive rationality guarantee. In practice, revealed preference bidding constraints are very demanding. We explain how approximate rationality can be used to create relaxed revealed preference constraints in an auction. We then show how combinatorial methods can be used to implement these relaxed constraints. Worst/best-case welfare guarantees that result from the use of such mechanisms can be quantified via the minimum/maximum virtual valuation function.