1. Consider the following simplified version of Google’s advertising auction. Assume that there are three bidders for a certain keyword and two positions for sponsored clicks. The bidders’ respective values per click are £60, £30 and £20. The valuations are common knowledge among bidders. The click-through rate for the top position is 400 clicks per hour, and for the second position it is x clicks per hour. a) In the generalised second-price (GSP) auction, for which x is it optimal for bidders to bid their respective value per click if all other bidders also bid their values per click? What is the revenue of the auction? How does it compare to the revenue in the Vickrey-Clarke-Groves (VCG) mechanism? b) Suppose that x = 200, and suppose that bidder 1 only bids a fraction α (α ≤ 1) of her value per click (and the other two bidders bid their full value per click). For which α is this an equilibrium in the generalised second-price auction? c) Suppose that x = 200, and suppose that all bidders only bid a fraction α (α ≤ 1) of their value per click (and this fraction is the same for all bidders). For which α is this an equilibrium strategy in the generalised second-price auction? For which α does the generalised second-price auction raise more revenue than the VCG mechanism?
1. Consider the following simplified version of Google’s advertising auction. Assume that there are three bidders for a certain keyword and two positions for sponsored clicks. The bidders’ respective values per click are £60, £30 and £20. The valuations are common knowledge among bidders. The click-through rate for the top position is 400 clicks per hour, and for the second position it is x clicks per hour. a) In the generalised second-price (GSP) auction, for which x is it optimal for bidders to bid their respective value per click if all other bidders also bid their values per click? What is the revenue of the auction? How does it compare to the revenue in the Vickrey-Clarke-Groves (VCG) mechanism? b) Suppose that x = 200, and suppose that bidder 1 only bids a fraction α (α ≤ 1) of her value per click (and the other two bidders bid their full value per click). For which α is this an equilibrium in the generalised second-price auction? c) Suppose that x = 200, and suppose that all bidders only bid a fraction α (α ≤ 1) of their value per click (and this fraction is the same for all bidders). For which α is this an equilibrium strategy in the generalised second-price auction? For which α does the generalised second-price auction raise more revenue than the VCG mechanism?
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1. Consider the following simplified version of Google’s advertising auction. Assume that there are three bidders
for a certain keyword and two positions for sponsored clicks. The bidders’ respective values per click
are £60, £30 and £20. The valuations are common knowledge among bidders. The click-through rate
for the top position is 400 clicks per hour, and for the second position it is x clicks per hour.
a) In the generalised second-price (GSP) auction, for which x is it optimal for bidders to bid their respective
value per click if all other bidders also bid their values per click? What is the revenue of the auction?
How does it compare to the revenue in the Vickrey-Clarke-Groves (VCG) mechanism ?
b) Suppose that x = 200, and suppose that bidder 1 only bids a fraction α (α ≤ 1) of her value per
click (and the other two bidders bid their full value per click). For which α is this an equilibrium
in the generalised second-price auction?
c) Suppose that x = 200, and suppose that all bidders only bid a fraction α (α ≤ 1) of their value
per click (and this fraction is the same for all bidders). For which α is this an equilibrium strategy
in the generalised second-price auction? For which α does the generalised second-price auction
raise more revenue than the VCG mechanism?
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