> My gut reaction to this auction system is that it would be vulnerable to abuse by a small number of bad actors. For example, what is to stop a company from bidding an artificially high amount in order to win the auction, knowing that they will most likely end up paying a more reasonable sum by the other fair bidders?
Because there is no incentive to bid higher than your true value.
Suppose you derive $N value from acquiring a user on the search screen. If you bid $N + x (where x > 0), then there are three cases:
1. Others bid more than $N + x, so you lose the action. In this case, the price was above the value you would derive, so not paying is the best choice.
2. Others bid between $N and $N + x. Let's call the action price $N + y. Then you win the auction. You pay $N + y for the user, but you only derive $N value, so you lose $y. This is a bad result; you shouldn't have paid.
3. Others bid less than $N. Let's call the auction price $N - z (where z > 0). Since you derive $N from the user, you gain $z, by paying, which is the best choice.
As a bidder, you want to avoid scenario 2. The best way to do this is to minimize the value of $x — that is; set $x = 0. So it's optimal to bid no higher than your true value, $N.
By analogy, you can also prove that it's suboptimal to bid below your true value by considering the three cases when you bid $N - x (where x > 0).
Because there is no incentive to bid higher than your true value.
Suppose you derive $N value from acquiring a user on the search screen. If you bid $N + x (where x > 0), then there are three cases:
1. Others bid more than $N + x, so you lose the action. In this case, the price was above the value you would derive, so not paying is the best choice.
2. Others bid between $N and $N + x. Let's call the action price $N + y. Then you win the auction. You pay $N + y for the user, but you only derive $N value, so you lose $y. This is a bad result; you shouldn't have paid.
3. Others bid less than $N. Let's call the auction price $N - z (where z > 0). Since you derive $N from the user, you gain $z, by paying, which is the best choice.
As a bidder, you want to avoid scenario 2. The best way to do this is to minimize the value of $x — that is; set $x = 0. So it's optimal to bid no higher than your true value, $N.
By analogy, you can also prove that it's suboptimal to bid below your true value by considering the three cases when you bid $N - x (where x > 0).