A Prior-independent mechanism (PIM) is a mechanism in which the designer knows that the agents' valuations are drawn from some probability distribution, but does not know the distribution.
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A typical application is a seller who wants to sell some items to potential buyers. The seller wants to price the items in a way that will maximize his profit. The optimal prices depend on the amount that each buyer is willing to pay for each item. The seller does not know these values, but he assumes that the values are random variables with some unknown probability distribution.
A PIM usually involves a random sampling process. The seller samples some valuations from the unknown distribution, and based on the samples, constructs an auction that yields approximately-optimal profits. The major research question in PIM design is: what is the sample complexity of the mechanism? I.e, how many agents it needs to sample in order to attain a reasonable approximation of the optimal welfare?
Single-item auctions
The results in imply several bounds on the sample-complexity of revenue-maximization of single-item auctions:
The situation becomes more complicated when the agents are not i.i.d (each agent's value is drawn from a different regular distribution) and the goods have limited supply. When the agents come from
Single-parametric agents
discuss arbitrary auctions with single parameter utility agents (not only single-item auctions), and arbitrary auction-mechanisms (not only specific auctions). Based on known results about sample complexity, they show that the number of samples required to approximate the maximum-revenue auction from a given class of auctions is:
where:
In particular, they consider a class of simple auctions called
Multi-parametric agents
study a market with different item types and unit demand agents.
study PIMs for the makespan minimization problem.
study a market with different item types. The supplies are fixed. The buyers can buy bundles of items, and have different valuations on bundles. They prove that, if
Alternatives
Prior-independent mechanisms (PIM) should be contrasted with two other mechanism types:
From the point-of-view of the designer, BOM is the easiest, then PIM, then PFM. The approximation guarantees of BOM and PIM are in expectation, while those of PFM are in worst-case.