Nylon Calculus

Nylon Calculus: NBA trades and auction theory

While auctions are not what most people think of around NBA general managers, some principles of auction theory could be used in governing negotiations of superstar trades.

When the general public thinks of an auction, basketball is not at all the first thing that comes to their mind. Shows like A&E’s Storage Wars, in which the contents of abandoned storage lockers are auctioned off to experts aiming to make a profit by undercutting the resale value of the items in the locker with their bids, have given auctions a wide audience. Even the Simpsons have an auction scene. Plenty of things pop up in people’s heads well before NBA basketball.

But auctions are also a very common game theory. The academic literature on them is extensive, covering about 58 years since William Vickrey wrote the paper that more or less starts auction theory — a paper that, among other things, led to Vickrey winning the 1996 Nobel Prize in Economics. Even beyond that, auctions themselves have been in use since no later than 500 BC, according to Herodotus, meaning that for most of human history, auctions have been a method of setting prices.

For the specific case we’re going to look at here, I’m going to quote Paul Klemperer’s summary of the auction theory literature: “[Auction theory] has been important in developing our understanding of… negotiations in which both the buyer and seller are actively involved in determining the price.”

At the most basic level, there are four types of auction: Ascending, descending, first-price sealed and second-price sealed. Several of those have varying names — the ascending is also known as the English auction, the descending is also known as the Dutch auction and the second-price sealed is known as the Vickrey auction — but for the sake of generally explaining these types of auctions, here’s a video from Numberphile and former Microsoft Economist Preston McAfee that breaks down what actually happens in those auctions mechanically.

That video also addresses a slight reduction in the number of cases we have to work with, because it shows that the ascending and descending auctions are close enough to the second-price sealed and first-price sealed, respectively, that for our purposes, I don’t mind referring to only two types of auction — first-price and second-price — based on whether the winner’s value or the second place’s value is determining the amount paid. Note that the winner’s value determining the price doesn’t necessarily mean that the winner’s value is the actual price since the winner might have attempted to bid lower in an attempt to pay less.

Now, to tie that to basketball. Consider the situation in which a superstar is up for a trade. We just finished months of trying to sort out an Anthony Davis trade that made sense, which was plain unpleasant for everyone involved, and the end price was, for lack of a better term, exorbitant. It seemed as though every subsequent time someone was adding additional news about the trade that had been agreed to, the Lakers had added another first-round pick to the deal.

Now think about that situation in terms of an auction. The Lakers, optimistically, paid the first-price’s value — that is, they paid an amount equal to what the highest bidder valued Davis at. I say optimistically because it’s entirely plausible that the Lakers paid more than their actual price and didn’t maximize their economic profit, but regardless. From what we’ve seen around the rest of the league, with none of the other truly viable alternative destinations submitting a bid that was competitive with the Lakers’ (i.e. the Celtics’ refusal to discuss Jayson Tatum), there’s clear separation between the first-price’s value and the second-price’s value, meaning we know which price they paid and it’s not the one that they want to.

Similarly, think about the trade discussions that followed Kemba Walker back in the 2018 offseason. The “best offer” that materialized in the news was the No. 8 overall pick and one of the Cavaliers’ dead salaries for the All-Star point guard, an offer that never had a chance in reality because the Cavs didn’t want to make an investment without assurance that LeBron James would return. Discussions around what the Hornets could get for Walker, then, revolved around the idea that since there was no other competitive bidder in the market, the price could be driven down. In other words, the market was being set by the second-price’s value. Discussions were revolving around simply beating the next highest bidder. A similar effect occurred with Jimmy Butler when he forced his way out of Minnesota, though I suspect that what the Timberwolves received may have been better than a strict second-price situation.

The sellers in the first case, where the price was set by the first-price’s value, made out much better than the sellers in the second case, where the price was set by the second-price’s value. In fact, if all bidders are acting rationally (which is a large “if”), the seller should always prefer if they can trigger a first-price auction setting, where the buyer should always prefer if they can trigger a second-price setting.

So now, let’s think about how the respective sides can actually trigger those settings. The way most people picture negotiations basically consists of offer and counteroffer that rubber bands towards a middle value. If the middle value is at or below the price of the buyer and at or above the price of the seller, then a trade happens. This is a logical negotiation pattern for both parties that probably builds cooperation, but it doesn’t necessarily lead to optimal results for either side. The buyer prefers that the price was at the value of the seller, where the seller prefers that the price was at the value of the buyer. In this case, since there are only two participants, and we know the buyer’s price is higher than the seller’s price, the buyer’s value is the first-price’s maximum value, and the seller’s value is the second-price’s value.

But that case really only works for a negotiation with only two participants. When you add in an additional participant, offer-counteroffer starts to look a little different because when the seller receives an offer from Buyer One, part of enticing a counteroffer from Buyer Two will contain providing a signal of the offer from Buyer One, because if Buyer Two’s offer doesn’t beat Buyer One’s then you have to take another offer-counteroffer step, reducing the price window that the end price rubber bands in into an interval more favorable towards that buyer.

As a result, the offer-counteroffer cycle turns into Buyers One and Two incrementing their offers to beat the other until one of them drops out. Which, given the article we’re in, should ring a rather large bell, because that’s exactly an ascending auction. And as you should also remember, the ascending auction produces a second-price value output, which is the worst case for the seller, despite the seller having coordinated the bidding. Since the seller can still go back to the strict offer-counteroffer once there are only two participants it ends up slightly better off than that, but generally speaking, it’s one of their worse outcomes.

At the same time, while that multi-party offer-counteroffer strategy is a buyer-favored strategy, they want to minimize the number of participants as much as possible, since more participants can only raise the value of the second price. In fact, the ideal number of participants for the buyer is two. Their best strategy is to keep only the seller’s and their own values relevant.

So then, in constructing a strategy for the buyer, their best strategy is to effectively construct a two-person auction with the seller as the other participant. They start with an offer that is low enough that the seller would never accept. They gradually increment it without taking counteroffers. When the price crosses the seller’s value, the seller should drop out of the auction by accepting the trade. This puts the value at the second-price value, and is the best case for the buyer.

The opposite is true of strategy traits for the seller. They are better off the more buyers participate, and therefore they should be trying to involve all 30 teams and somehow piercing the CBA to include Real Madrid. They also need to find a path to a first-price auction.

So a strategically optimal strategy for the seller, then, is to construct as many offers as possible that they are indifferent between, starting with offers that are far more valuable than anyone would accept. Then, they start decreasing the value of the offers until a team decides to accept. This functions like a Dutch auction, and therefore produces the first-price value.

But those strategies are both vulnerable to bluffing. The buyer’s strategy can be gamed by a seller who assumes that offers will not come off the table, so if that seller simply pretends that there’s still another bidder and waits until the buyer no longer is willing to increment their price up, the seller can assume they are at the buyer’s value and get the first-price value out of a second-price strategy.

Similarly, if a specific buyer has the highest value and assumes that they’ll have the chance to retroactively beat any winning offer, they can simply decline offers even once the bid passes their value and then offer to beat the winning offer once the next price is reached. If that happens, then the buyer will have gotten second-price value out of a first-price strategy. In neither case does the disadvantaged part actually lose the trade according to their private value, since the first-price and second-price are both going to be at or below the price where they’re indifferent about making the trade, but they could’ve done better had their strategy not been beaten.

Let’s propose, then, an additional strategy for the seller that gives them a solution to that bluff. The buyer doesn’t have a clear path to beating a bluffing seller, because they can’t restrict offers as easily, but the seller has enough control over the process to be able to conduct a sealed bid auction. When the seller conducts a sealed bid auction, they negate the ability of the buyer to bluff in the manner described, because the higher-valued buyer no longer has the ability to retroactively beat the new price. This also has the added benefit that it doesn’t require the team’s CBA guys to construct approximately 500 offers in a short span of time.

Next: The Encyclopedia of Modern Moves

Those two strategies then, which kind of reveal how seller-favored the market should be, present a path towards better strategy in trade negotiations. Even though they only broach the absolute surface of how auction theory can impact trades, the patterns of thought involved here can lead to far more effective transactions from teams that adopt them. And there’s still far further to go with this line of thought — auction theory has far more expansive literature than I addressed here, and basketball has far more cases than the things already considered can be applied to than just the singular case of the superstar.

But since analytics are, as Seth Partnow, former director of analytics for the Bucks, says, “an effort to seek most advantageous manner of playing under current conditions,” teams should absolutely be adopting the concepts involved and attempting to negotiate with the auction structure in mind even with just what we know so far.

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