Bayesian-optimal mechanism

Bayesian optimal mechanism design (BOMD) is a challenge in mechanism design and auction theory.

A typical application is a seller who wants to sell an item in an auction. There are many different types of auctions, and the seller wants to design the auction rules in a way that will maximize his profits. Naturally, the profits depend on the amount that each buyer is willing to pay for the item. The seller does not know these amounts, but he assumes that they are drawn from a certain known probability distribution. The phrase "Bayesian optimal mechanism design" has the following meaning:^[1]^{: 335–338}

Bayesian means that we know the probability-distribution from which the agents' valuations are drawn (in contrast to prior-free or worst-case mechanisms, which do not assume any prior probability distribution).
Optimal means that we want to maximize the expected revenue of the auctioneer, where the expectation is over the randomness in the agents' valuations.
Mechanism design means that we want to design rules that define a truthful mechanism, in which each agents has an incentive to act according to his true value.

^ Vazirani, Vijay V.; Nisan, Noam; Roughgarden, Tim; Tardos, Éva (2007). Algorithmic Game Theory (PDF). Cambridge, UK: Cambridge University Press. ISBN 0-521-87282-0.

[agt-1] Vazirani, Vijay V.; Nisan, Noam; Roughgarden, Tim; Tardos, Éva (2007). Algorithmic Game Theory (PDF). Cambridge, UK: Cambridge University Press. ISBN 0-521-87282-0.

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