Virtual valuation

In other words, the intermediary offers the object to the buyer with the highest virtual valuation so long as it is above the reserve price. While the... 

Clearly, the buyer s marginal revenue is identical to her virtual valuation (3.37). In setting up the reserve price, the intermediary may be thought of as a buyer with a value and marginal revenue of zero. Thus, the intermediary offers the object to the buyer with the highest marginal revenue so long as it is positive (above her own). 

Recall that fi -) is the probability distribution over the type of agent i, and Fi -) the cumulative distribution. This priority level, sometimes called the virtual valuation, is less than an agent s type by the expectation of the second-order statistic of the distribution over its type. Economically, one can imagine that this represents the information rent of an agent, the expected payoff that an agent can extract from the private information that it has about its own type. 

Mineral exploration, the search for economic ore deposits, requires somewhat different reference samples than those used in ore valuation. Soil or sediment and water samples are frequently used in the search when mineralized areas of abundant outcrop or those covered only by thin locally derived overburden are being evaluated. In such cases, it is virtually impossible not to detect the mineralization from an analysis of ore elements in these types of samples. Later, as the mineral deposits closest to the surface were exploited and then played out, new deposits occurred at progressively greater depths, and these sample types were less and less effective as markers in the search (Hoffman 1989). 

By the revelation principle (Section 3.2), it is sufficient to consider an incentive compatible direct mechanism. In other words, regardless of the mechanism constructed by the intermediary, given the equilibrium of the mechanism, we can construct an equivalent incentive compatible direct mechanism, where the buyer and the supplier report their respective valuations to the intermediary, and the intermediary determines if the trade is to take place. If so, she determines the buyer s payment and the suppliers revenue. Otherwise, the players take their outside options in a direct matching market. Let T(/3,p, w) represents the direct revelation mechanism, where /3(s, v) is the probability that the trade will take place, p(s, v) is the expected payment to be made by the buyer to the intermediary (the asked price), and w(s, v) is the expected payment from the intermediary to the supplier (the bid price), where s and v are the valuations given by the supplier and buyer, respectively. As mentioned above, the intermediary is aware of the buyer and the supplier s outside options as random variables characterized by distributions G and F, respectively. Based on this information the intermediary establishes the buyer s virtual willingness to pay follows ... 

In essence, to maximize her own profit the intermediary must restrict the trade to profitable situations, as indicated by the difference between the buyer s virtual willingness to pay and the supplier s virtual opportunity cost. For instance, suppose s and v are both uniformly distributed on the unit interval. Then, based on the above mechanism the trade takes place if and only if 5(1 ) = 2v — 1 >2s = 5(5). Or equivalently, v — s >., i.e., the trade takes place iff the buyer s valuation exceeds the supplier s valuation by... 

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