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In auction theory, particularly Bayesian-optimal mechanism design, a virtual valuation of an agent is a function that measures the surplus that can be extracted from that agent.
A typical application is a seller who wants to sell an item to a potential buyer and wants to decide on the optimal price. The optimal price depends on the valuation of the buyer to the item, v {\displaystyle v}. The seller does not know v {\displaystyle v} exactly, but he assumes that v {\displaystyle v} is a random variable, with some cumulative distribution function F {\displaystyle F} and probability distribution function f := F ′ {\displaystyle f:=F'}.
The virtual valuation of the agent is defined as: