eBay’s Recommendation: 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, $0.01) above the second highest proxy bid. For example, imagine that three people have placed bids on a used laptop of $50, $90, and $100. The current price will be at $90.01, and if the auction ended the player who bid $100 would win at a price of $90.01. If you were to place a bid of $95 then the player who bid $100 would still win, but at a price of $95.01, while if your bid was $110 then you would win at a price of $100.01. 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 other bidders value it. (a) Argue that bidding more than your valuation is weakly dominated by actually bidding your valuation. (b) Argue that bidding less than your valuation is weakly dominated by actually bidding your valuation. (c) Use your analysis to make sense of eBay’s recommendation. Would you follow it?

eBay’s Recommendation: 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, $0.01) above the second highest proxy bid. For example, imagine that three people have placed bids on a used laptop of $50, $90, and $100. The current price will be at $90.01, and if the auction ended the player who bid $100 would win at a price of $90.01. If you were to place a bid of $95 then the player who bid $100 would still win, but at a price of $95.01, while if your bid was $110 then you would win at a price of $100.01. 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 other bidders value it. (a) Argue that bidding more than your valuation is weakly dominated by actually bidding your valuation. (b) Argue that bidding less than your valuation is weakly dominated by actually bidding your valuation. (c) Use your analysis to make sense of eBay’s recommendation. Would you follow it?