Dominant Strategy in English Auction
1. Consider the following ascending price auction for some good. Each bidder starts with his or her finger on a button. The price starts to rise automatically (imagine it is shown on a screen), starting from v0. The bidders watch the rising price and, when a bidder no longer wishes to participate, he or she lifts his or finger from the button. Once he or she has lifted his
or her finger, he or she is out of the auction for good (i.e., no one can go back in). As soon as only one button is being pressed (i.e., as soon as the next-to-last bidder exits), the auction stops and the bidder still pressing his or her button gets the good at the price shown on the screen. Assume that the good in question is a pure private-value good; that is, its value to
an individual bidder is independent of its value to any other bidder. Each bidder has a value v, which is drawn from the interval [v0, v1] according to a known distribution.
(a) There is a dominant strategy for bidders to use in this auction. What is it?
(b) Show by example that any strategy other than the dominant strategy yields a strictly lower payoff than the dominant strategy in some circumstances.