This example, okay? We've got three bidders with ten, five,

one being the R's, . And three ad spaces with five, three, one

as the click through rates. So before we forget, let's write those

down, okay? Ten, five, one.

And five, three, one, okay? So now let's finish the discussion of this

example. What kind of bidding will they provide?

Let's assume they do truthful bidding. The keyword is assume.

We'll later come back to why this is not in generally in channel two.

But assuming that they do truthful bidding, then their bids are exactly ten,

five, one, respectively out of the three buyers.

Okay. So, in that case, we know exactly how much

they'll bid. They'll bid $50, and $30, and $ten for the

three ad spaces by the first user. The second user will bid five x five, $25,

fifteen, and $five for the three s-, ad spaces.

The third one will bid five, three, one for the three ad spaces.

Those are the bids. Okay?

50, 30, ten. 25, fifteen.

Five and 531. And the allocation is simple.

Okay, first one get this one, second get this one, third one get this one.

What about the charging? So the charging basically is that the

first one would be charged by this. It's 25 clicks, dollars per click.

Second one will be charged by The bidder, the bid from the third, bidder, on the

second space. So it would be charged three.

The last one would be charged the very small minimum, which is.5 in this case.

Okay? These are in dollar amounts.

Per click. So now we can take look at the revenue.

So, Google collects the following revenue: which is 25 from the first bidder, three

from the second, and .5 from the third, which is $28.5.

And then the payoff to the buyers. The three buyers.

So have to make three calculations. Remember, a payoff u equals valuation v

minus price p. So, for the first one, you've got the,

ties the spot. So, your valuation, 'tis ten.

Subtract the price you pay, which is five per click, equals five per click.

Or equivalently. $Five per click times five clicks per hour

on average is $25 per hour. And the second bidders payoff is $five

minus one. That's your valuation and that's the price

you pay. So what you get is $four that's per click.

Which translates into $four times three clicks per hour, that is $twelve per hour.

Finally, the third one your valuation for the third ad space that you received is

one and the price you pay is the minimum. So the payoff is half a dollar per click

which translates into half a dollar per click times one click per hour which is

half a dollar per hour. So the total payoff is $25 per hour for

the first bidder, +12for the second bidder, + half for the third bidder, which

is 37.5. And this is in per hour, just like here,

per hour, cuz it reflects both. The payoff per click and the expected

number of clicks per hour. So this is how much Hugo is receiving in

the revenue and this is how much net happiness payoff is received by the three

bidders all together. So you may think GSP sounds pretty good.

It's pretty simple to explain the allocation and the charging, and as long

as we can assume they do truthful bidding seems to be a pretty efficient allocation

system except we cannot assume that people will do truthful bidding, 'kay?

So here's a very simple example. I can write it in the margin of the slide.

Let's say there are, there's two ad spaces.

The top one get 400 clicks per hour. The next one gets 300 clicks per hour.

Okay, both are pretty powerful but the first one it's lightly better.

And there are three bidders, one, two and three.

Their valuation which is the number of dollars per click expected is $twelve,

$eight and $four respectively. Now, let's say, what should the first

bidder do? Let me think.

Well, maybe she should bid a truthful bidding.

So, she should bid twelve, or equivocally twelve times 400 for the first spot,

twelve times 300 for the second spot. But, actually, if that's what she does.

Okay. She's going to win the first spot.

And the valuation in that case or the payoff, I'm sorry, in that case, is the

valuation twelve minus the price you pay, just by GSP eight.