My brother-in-law wanted to sell something with an auction but first he wanted to assemble as many interested buyers as he could. His problem is that while he knew there were many interested buyers in the world he didn’t know who they were or how to find them. But he had a good idea:  people who are interested in his product probably know other people who are also interested. He asked me for advice on how to use finders’ fees to incentivize the buyers he already know about to introduce him to any new potential buyers they know.

This is a very interesting problem because it interacts two different incentive issues. First, to get someone to refer you to someone they know you have to confront a traditional bilateral monopoly problem. You are a monopoly seller of your product but your referrer is a monopoly provider of access to his friend because only he knows which and how many of his friends are interested. If your finder’s fee is going to work it’s going to have to give him his monopoly rents.

The interesting twist is that your referrer has an especially strong incentive not to give you any references. Because anybody he introduces to you is just going to wind up being competition for him in the auction for your product.  So your finder’s fee has to be even more generous in order to compensate your referrer for the inevitable reduction in the consumer’s surplus he was expecting from the auction.

I told my brother-in-law not to use finder’s fees.  That can’t be the optimal way to solve his problem.  Because there is another instrument he has at his disposal which must be the more efficient way to deal with this compound incentive problem.

Here’s the problem with finder’s fees.  Every dollar of encouragement I give to my buyers is going to cost me a full dollar.  But I have a way to give him a dollar’s worth of encouragement at a cost to me of strictly less than a dollar.  I leverage my monopoly power and I use the object I am selling as the carrot.

In fact there is a basic principle here which explains not only why finder’s fees are bad incentive devices but also why employers give compensation in the form of employee discounts, why airlines use frequent flier miles as kickbacks and why a retailer would always prefer to give you store credit rather than cash refunds. It costs them less than a dollar to provide you with a dollar’s value.

Why is that?  Because any agent with market power inefficiently under-provides his product.  By setting high prices, he creates a wedge between his cost of supplying the good and your value for receiving it.  If he wants to do you a favor he could either give you cash or he could give you the cash value in product.  It’s always cheaper to do the latter.

So what does this say about incentivizing referrals to an auction?  How do you “use the object” in place of a finder’s fee?  The optimal way to do that is the following.  You tell your potential referrer that you will give him an advantage in the auction if he brings to you a new potential buyer.  Because you are a monopoly auctioneer there is always a wedge that you can capitalize on to do this at minimal cost to yourself.

In this particular example the wedge is your reserve price.  Your referrer knows that you are going to extract your profits by setting a high reserve price and thereby committing not to sell the object if he is not willing to pay at least that much.  You will induce your referrer to bring in new competition by offering to lower his reserve price when he does.

Now of course you have to deal with the problem of collusion and shills.  Of course that’s a problem in any auction and even more of a problem with monetary finder’s fees but that’s a whole nuther post.

(Ongoing collaboration with Ahmad Peivandi)