Question

Global TV implements Varian’s Position Auction for commercial spots during the evening news. The highest bidder is to be awarded the first commercial spot which is known to attract 2000 viewers and the second-highest bidder is to be awarded the second commercial spot which is known to attract only 500 viewers. They use a position auction (GSP) mechanism: the highest bidder will pay a price equal to bid of the second-highest bidder and the second-highest bidder will pay a reserve price of 2 dollars. There are two bidders: Dodge Motor Company who have a valuation of 6 dollars per viewer and Ford Motor Company who have a valuation of 4 dollars per viewer. what is the outcome of this bid?

Answer 1

The Generalized Second Price (GSP) auction is an auction mechanism for awarding bids. In this mechanism, the bidders place bids and the highest bidder gets the first slot, the second highest bidder gets the second slot and so on. The highest bidder pays a price equal to the bid price of the second highest bidder, the second highest bidder pays a price equal to the bid price of the third highest bidder so on. This model is based on complete information i.e. all the participants have complete information about the market and about the valuation of other bidders.

Here, there are two commercial spots during evening news and two bidders. The highest bidder would get the first spot attracting 2000 viewers and the second highest bidder would get the second spot attracting 500 viewers.

There are two bidders : Dodge Motor Company who have a valuation of 6 dollars per viewer and Ford Motor Company who have a valuation of 4 dollars per viewer. Now, it is to be expected that the company having higher valuation will bid higher and will get the first spot while paying the bid price of second highest bidder whereas the person having lower valuation will bid lower and will get the second spot while paying the reservation price of 2 dollars.

Since, Dodge Motor Company has a valuation of 6 dollars per viewer which is higher than Ford Motor Company's valuation of 4 dollars per viewer, so Dodge Motor Company will bid any price higher than 4 dollars per viewer and less than or equal to 6 dollars per viewer and will become the first highest bidder and get the first spot. It's important that they bid greater than 4 dollar, otherwise the bid would go to Ford motor Company and they will bid less than 6 dollars which is their valuation as bidding higher than their valuation will lead to losses for them.

Ford motor Company would bid any price between 2 dollars to 4 dollars and will become the second highest bidder getting the second slot. It will be greater than or equal to 2 dollars as 2 dollars is the reserve price (reserve price is the price which would make the person auctioning indifferent between selling and not selling), and it will be less than or equal to 4 dollars per viewer which is their valuation as bidding higher than valuation would cause losses for Ford motor Company.

Since Dodge motor company is the highest bidder so it will pay the price of the second highest bid which is 4 dollars per viewer and will get the first slot. Whereas, Ford Motor company which is the second highest bidder will pay the reserve price of 2 dollars per viewer and would get the second spot. All this was possible because the bidders had complete information.

This is the outcome of the bid.