Consider a second-price auction in which the seller has an art object for sale. There are...

 

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Consider a second-price auction in which the seller has an art object for sale. There are two potential buyers (bidders) whose valuations of the object are 0<v, <v, and these valuations are common knowledge. The bidders simultaneously submit bids s, 20 and the highest bidder wins the object and pays the second bid, i.e., if he wins, a bidder's utility is u, =v, - max S,, and the other bidder pays nothing (and gets utility zero). If the bidders bid the same, the art object is allocated among them by tossing a fair coin. Show that for each player the strategy of bidding one's true valuation s, =v, weakly dominates all other strategies. Consider a second-price auction in which the seller has an art object for sale. There are two potential buyers (bidders) whose valuations of the object are 0<v, <v, and these valuations are common knowledge. The bidders simultaneously submit bids s, 20 and the highest bidder wins the object and pays the second bid, i.e., if he wins, a bidder's utility is u, =v, - max S,, and the other bidder pays nothing (and gets utility zero). If the bidders bid the same, the art object is allocated among them by tossing a fair coin. Show that for each player the strategy of bidding one's true valuation s, =v, weakly dominates all other strategies.