An Inverse Optimization Based Auction Mechanism to Support a Multi Attribute Rfq
An Inverse Optimization Based Auction Mechanism to Support a Multi Attribute Rfq
Lawrence M Wein
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01, the auctioneer's utility is i'liq*)"^^ +i'3q* -Oiiq* -0i2{q*f -9a3{q*y^ -t^* -t = 2. 3909, the winning suppHer's profit is tt* + e = 0. 6327, and the total surplus is 3. 0236. 20 Figure 1: True value, supplier I's cost Ci, supplier 2's cost C2, minimum enforceable price p, and the optimal scoring rule (• • • ) versus quality. To illustrate the effects of inducible competition, we next consider a "high-competition" example in which the parameters for supplier I's cost and the true value func...tions are unchanged, but we set $21 = 2, ^22 = 1, and 623 = 0; the cost curves, the true value function, and the resulting minimum enforceable prices are shown in Figure 2. Running the optimization (15)-(17), (48) under the new parameters for suppher 2 results in q* — 0. 8482 and TX* = 0. 1000 = e. If we enforce {c\{q*) + tt* + e, q*) (see Figure 2), the payoff to the auctioneer is 3. 2627, which is roughly 35% greater than in the previous example. Referring to Figure 2, notice that co crosses the line tangent to C\ at ci's "elbow, " which allows the auctioneer to enforce near-cost prices just past where the elbow starts.
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