We will take a first glimpse at applying game theory to confront the incentive problem and understand the design of efficient mechanisms.  The simplest starting point is the efficient allocation of a single object.  In this lecture we look at efficient auctions.  I start with a straw-man:  the first-price sealed bid auction.  This is intended to provoke discussion and get the class to think about the strategic issues bidders face in an auction.  The discussion reaches the conclusion that there is no dominant strategy in a first-price auction and it is hard to predict bidders’ behavior.  For this reason it is easy to imagine a bidder with a high value being outbid by a bidder with a low value and this is inefficient.

The key problem with the first-price auction is that bidders have an incentive to bid less than their value to minimize their payment, but this creates a tricky trade-off as lower bids also mean an increased chance of losing altogether.  With this observation we turn to the second-price auction which clearly removes this trade-off altogether.  On the other hand it seems crazy on its face:  if bidders don’t have to put their money whether mouths are won’t they now want to go in the other direction and raise their bid above their value?

We prove that it is a dominant strategy to bid your value in a second-price auction and that the auction is therefore an efficient mechanism in this setting.

Next we explore some of the limitations of this result.  We look at externalities:  it matters not just whether I get the good, but also who else gets it in the event that I don’t.  We see that a second-price auction is not efficient anymore.  And we look at a setting with common values:  information about the object’s value is dispersed among the bidders.

For the comon-value setting I do a classroom experiment where I auction an unknown amount of cash.  The amount up for sale is equal to the average of the numbers on 10 cards that I have handed out to 10 volunteers.  Each volunteer sees only his own card and then bids.  If the experiment works (it doesnt always work) then we should see the winner’s curse in action:  the winner will typically be the person holding the highest number, and bidding something close to that number will lose money as the average is certainly lower.

Here are the slides.

(I got the idea from the winner’s curse experiment from Ben Polak, who auctions a jar of coins in his game theory class at Yale.  Here is a video. Here is the full set of Ben Polak’s game theory lectures on video.  They are really outstanding.  Northwestern should have a program like this.  All Universities should.)