Description
Suppose there are 2 ad slots each with its own clickthrough rate:
Slot Click Through Rate
a 10
b 7
And suppose there are 3 advertisers:
Advertiser Valuation Per Click
x 10
y 9
z 2
We also suppose that the search engine assigns ad slots using a Gnereralized Second-Price (GSP)
auction, and answer the following questions:
1. In this problem, is truthful bidding a Nash equilibrium? To receive full credit, you must
either prove that truthful bidding is a Nash equilibrium or show which advertiser(s) could
profit by changing their bid away from truthful bidding.
Answers:
1. ANSWER 1
2. Find a Nash equilibrium for this problem (without truthful bidding) in which the total advertiser valuation is maximized (i.e., advertiser x is assigned slot a and advertiser y is assigned
slot b). You may use any technique you want to find this Nash equilibrium, but you must
convince me that it is an actual Nash equilibrium.
Answers:
2. ANSWER 2
3. Create a new sponsored search problem with at least 2 slots and at least 3 bidders in which
truthful bidding is a Nash equilibrium.