Bid Shading – Game Theory Application
This article discusses a new form of auctioning in programmatic advertising – bid shading. Traditionally, these transactions have been mostly second-price auctions, that is, the highest bidder only has to pay the second highest bid. For example, if there are two potential buyers in the market and one bids $15 while the other bids $10, the winner (who is the one who bid $15) only has to pay $10 to secure the good. However, there has recently been a shift to first-price auctions, which is when the highest bidder pays his bid. In this case, the highest bidder will pay $15 to secure the good.
In the case of bid shading, a computer will generate a middle ground between the highest and second-highest bid through analyzing the history and database of bids. This will hopefully help to minimize the chances of buyers overpaying.
I believe that auctions are excellent examples of the real-life application of game theory.
For all three auction situations, game theory comes into play when the buyers decide what bids they are going to offer for the item. Let us arbitrarily set the value of the good to be $10. In the case of a first-price auction – if player 1 decides to bid $1, player 2 can always increase the bid to $2 to secure the item and result in an added utility of $8 to the player. Player 1 knows that in this situation, he will have the overall utility of $0 so he will logically choose to increase the bid to greater than $2. This continues till one of the players bids $10. The other player can choose to bid $10.01, but even though he will end up with the auctioned item, he will have an overall utility of -$0.01 because the good is only valued at $10. He logically decides he is better off just bidding $10, and even though he might not get the good, an overall utility of $0 is better than -$0.01.
In the case of a second-price auction, if player 1 decides to start off bidding with $1 again, player 2 can choose to bid anything higher than $1 because he knows his overall utility will end up being $9. Of course, as a rational economic agent, player 1 will choose to out-bid player 2, till the point that the bid reaches $10. Then, he can choose to bid $11 and pay $10 for the good, but since the bids are not disclosed, he also has the fear the player 2 bids something higher than the value of the good but lower than his own bid, same goes for bid shading. Hence, the buyers are incentivized to bid the actual value of what the item is worth, creating a Nash Equilibrium.
Of course, in reality, it is not going to be as transparent as this theoretical case because different people play different values on the same product. Especially in the situation that is described in the article, programmatic advertising is a service that does not have a fixed value for any potential buyer. Hence, it will be hard for players to logically deduce the bids others will give. In this case, I think it is less of game theory, but more of the work of the middleman.