are n bidders. Bidder i values the first unit that she obtains at v; and the second unit at w¡, where v¡ > w¡ > 0. Each bidder submits two bids; the two highest bids win. Retain the tie-breaking rule in the text. Show that in discriminatory and uniform-price auctions, player i's action of bidding v; and w; does not dominate all her other actions, whereas in a Vickrey auction it does. (In the case of a Vickrey auction, consider separately the cases in which the other players' bids are such that player i wins no units, one unit, and two units when her bids are v; and w¡.)
are n bidders. Bidder i values the first unit that she obtains at v; and the second unit at w¡, where v¡ > w¡ > 0. Each bidder submits two bids; the two highest bids win. Retain the tie-breaking rule in the text. Show that in discriminatory and uniform-price auctions, player i's action of bidding v; and w; does not dominate all her other actions, whereas in a Vickrey auction it does. (In the case of a Vickrey auction, consider separately the cases in which the other players' bids are such that player i wins no units, one unit, and two units when her bids are v; and w¡.)
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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![EXERCISE 87.1 (Multi-unit auctions) Two units of an object are available. There
are n bidders. Bidder i values the first unit that she obtains at v; and the second
unit at w₁, where vi > w; > 0. Each bidder submits two bids; the two highest
bids win. Retain the tie-breaking rule in the text. Show that in discriminatory and
uniform-price auctions, player i's action of bidding v; and w; does not dominate
all her other actions, whereas in a Vickrey auction it does. (In the case of a Vickrey
auction, consider separately the cases in which the other players' bids are such that
player i wins no units, one unit, and two units when her bids are v; and w;.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fac709e92-d5bf-4722-a44f-338534d5d3fb%2F8bd81b38-b0f9-472a-b11a-1ec6d571059e%2F24zasab_processed.png&w=3840&q=75)
Transcribed Image Text:EXERCISE 87.1 (Multi-unit auctions) Two units of an object are available. There
are n bidders. Bidder i values the first unit that she obtains at v; and the second
unit at w₁, where vi > w; > 0. Each bidder submits two bids; the two highest
bids win. Retain the tie-breaking rule in the text. Show that in discriminatory and
uniform-price auctions, player i's action of bidding v; and w; does not dominate
all her other actions, whereas in a Vickrey auction it does. (In the case of a Vickrey
auction, consider separately the cases in which the other players' bids are such that
player i wins no units, one unit, and two units when her bids are v; and w;.)
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