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1. Show formally that to bid one's own value is a dominant strategy in the Vickrey auction.
2. Suppose we have an auction in which every bidder pays his bid whether or not he wins the object. Find the equilibrium strategies in this case if there are n bidders and the distribution is uniform. (This auction format is called an all-pay auction for obvious reasons.)
3. Suppose there are two bidders and the distribution is uniform. Suppose if you win or not you pay the second highest bid. Find the equilibrium strategies. What is peculiar about them? (This auction format is referred to as the war of attrition.)
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Caselet on McDonald’s vs. Burger King - Waiting time
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