The Value of Negotiation
Evidence from used car markets
What is the value that negotiators create? Is it fundamentally a zero-sum conflict, where hiring a better negotiator allows you to extract more from your adversary, and everyone would be better off if nobody were allowed to hire negotiators at all? Or does it create value, making transactions which would never otherwise occur happen, and move prices to their competitive optimum?
A recent paper from Bradley Larsen, Carol Hengheng Lu, and Anthony Lee Zhang studies the effect of intermediaries on sales in used car markets. These are large, dealer-to-dealer purchases of used cars, such as when a rental car agency wishes to dispense with part of their stock. Auctions are ascending auctions (the classic, “I have ten, give me fifteen, I have fifteen” type) with a reserve price — that is, one where buyers are not willing to sell below. If the bidding does not exceed the reserve price, then the interested parties negotiate, commonly employing an intermediary to pass along information over the phone.
What is really cool is that, while intermediaries have no effect on the price that the cars end up being sold at, more experienced intermediaries increase the likelihood that a sale occurs, and make the negotiation process faster too. This is a bit odd — the intermediaries possess no secret information over people’s prices, nor are they particularly negotiating — they simply pass along offers and counteroffers over the phone.
Consider the perspectives of the buyer and seller. Both of them have private information which neither wishes to reveal. If the buyer knew the exact price below which seller would not sell, then he would offer a take-it-or-leave-it offer at exactly that price. Knowing you wouldn’t get any better, the seller would take it; and of course, the opposite applies to the buyer. Knowing this, it is optimal to commit to not taking some offers which are mutually beneficial, but not income maximizing in the long run. The condition that no party is able to achieve a better pay out by changing their strategy is called “incentive compatibility”.
This leads us to the Myerson-Sattherthwaite theorem. Suppose there are two parties, a seller and a buyer, who both value the good at a random value between 0 and 1. Given this, there is no mechanism which can be simultaneously incentive compatible, be individually rational, have a balanced budget, and make all mutually beneficial trades happen. This means that everyone behaves in the selfishly optimal way; that the expected value to everyone is greater than or equal to zero; and that there are no outside funds employed to patch things over.
Think about it like this. In a Myerson auction, which is the optimal auction format for a monopolist selling one good a single time, the seller gives a take-it-or-leave-it offer at the midpoint of each buyer’s distribution. The seller is assumed to have a value of zero and the buyers a value randomly drawn between some values, say 0 and 1. Under this, there is a way to guarantee that all mutually beneficial trades happen — require that the price be no higher than just above zero. You have made all trades occur by guaranteeing all of the surplus to the buyer. When the valuations overlap, you must guarantee all of the surplus to the seller too, which obviously cannot be done. One can get around it by violating the balanced budget constraint, and use outside money to subsidize it.
So what’s going on in the used car market? The intermediary is not subsidizing the market, but they do have choice over which values and which offers they report. The experienced negotiators are better able to tell which offers ought not be reported, hence why they don’t have much impact on price. They don’t care about who gets a bigger share, just whether the deal closes, and this gives them credibility. In a world of incomplete information — which is to say, all of them — intermediaries and negotiators are positive sum.