Homework5 - Stanford University Management Science and...

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Stanford University Management Science and Engineering MS&E 260 Fall 2016 Homework #5 1/3 MS&E 260: Introduction to Operations Management HOMEWORK #5 Due November 30, 2016 1. (50 pts) You are running a 2 nd price auction and there are 5 bidders. Bidders valuations are privately known to bidders and are drawn independently from U[0,80]. a. (7 pts) Suppose your valuation is 30, how would you bid in this auction? b. (9 pts) What is the expected revenue for the seller in this auction? (Recall that the seller only knows the distribution but not the values). Remark: the revenue in a second price auction when one only bidder bids above the reserve price. In all the parts c-f below you can use simulations. c. (10 pts) You are interested in setting a reserve price that approximates the optimal expected revenue. In a 2 nd price auction with a reserve price, the item is allocated to the highest bidder only if his bid is above the reserve price, in which case his payment is max(reserve price, 2 nd highest bid). If no one bids above the reserve price, the item is not allocated. [So this is like a 2 nd price auction in which the auctioneer placed a bid r].
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