ps5.pdf - Game Theory for Business Assignments Problem Set 5 Due on April 23rd by the start of class Question 1 eBay\u2019s Recommendation It is hard to

# ps5.pdf - Game Theory for Business Assignments Problem Set...

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Game Theory for Business Assignments Problem Set 5 Due on April 23 rd by the start of class Question 1: eBay’s Recommendation It is hard to imagine that anyone is not familiar with eBay, the most popular auction website by far. In a typical eBay auction a good is placed for sale, and each bidder places a ‘proxy bid’ which eBay keeps in memory. If you enter a proxy bid that is lower than the current highest bid, then your bid is ignored. If, however, it is higher, then the current bid increases up to one increment (say, 1 cent) above the second highest proxy bid. For example, imagine that three people have placed bids on a used laptop of \$55, \$98, and \$112. The current price would be \$98.01, and if the auction ended the player who bid \$112 would win at a price of \$98.01. If you were to place a bid of \$103.45 then the player who bid \$112 would still win, but at a price of \$103.46, while if your bid was \$123, then you would win at a price of \$112.01. Now consider eBay’s historical recommendation that you think hard about the value you impute to the good, and that you enter your true value as your bid—no more, no less. Assume that the value of the good for each potential bidder is independent of how much the other bidders value it. (a)