Abstract
In unrestricted combinatorial auctions, we put forward a mechanism that guarantees a meaningful revenue benchmark based on the possibilistic beliefs that the players have about each other’s valuations. In essence, the mechanism guarantees, within a factor of two, the maximum revenue that the “best informed player” would be sure to obtain if he/she were to sell the goods to his/her opponents via take-it-or-leave-it offers. Our mechanism is probabilistic and of an extensive form. It relies on a new solution concept, for analyzing extensive-form games of incomplete information, which assumes only mutual belief of rationality. Moreover, our mechanism enjoys several novel properties with respect to privacy, computation and collusion.
Highlights
We study the problem of generating revenue in unrestricted combinatorial auctions, solely relying on the players’ possibilistic beliefs about each others’ valuations
In order to analyze it in settings where the players have possibilistic beliefs, we propose a new and compelling solution concept that only assumes mutual belief of rationality, where the notion of rationality is the one considered by Aumann [15]
Because privacy is important to many strategic agents, we hope that trying to preserve it will become a standard goal in mechanism design
Summary
We study the problem of generating revenue in unrestricted combinatorial auctions, solely relying on the players’ possibilistic beliefs about each others’ valuations. For unrestricted combinatorial auctions, no known mechanism guarantees any significant revenue benchmark in settings of incomplete information. In complete information settings (where the players have common knowledge about their valuations), assuming common knowledge of rationality, [7,8,9] have designed mechanisms that guarantee revenue arbitrarily close to the maximum social welfare. For unrestricted combinatorial auctions, we construct a mechanism that guarantees, within a factor of two, another interesting revenue benchmark, BB, solely based on the players’ possibilistic beliefs. Let BBi (for “best belief”) be the maximum social welfare player i can guarantee, based on his/her beliefs, by assigning the goods to his/her opponents. For a detailed discussion about these properties of our mechanism, see Section 6.2
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