The 'Dilemma' at hand in NBA lockout

It seems incomprehensible. Unable to agree on how to split a $4 billion pie, the NBA players and owners are now letting that pie go to waste, making everyone go hungry.

When talks ended Monday night without an agreement, the league wasted no time in canceling the first two weeks of the 2011-12 regular season. Their hopes currently rest on mediation, which is now scheduled for next week. Failing that, the two sides are expected to retreat and regroup, with the next round of cancellations probably just around the corner.

How could they let this happen? They were so close -- according to most reports, the league offered the players 50 percent of revenues, with the players holding firm at 53 percent. Why couldn't they split the difference? Instead of dividing that last $120 million down the middle, the two sides dug in.

The consequences are enormous, as David Stern might say. Holding out collectively costs the players more than $82 million per week. The players have already burned through all they stood to gain this season had they agreed to owners' offer of 50 percent, and will hit the break-even point on a six-year agreement if they don't settle by Dec. 16. The owners will also lose money -- some estimates are as high as $1 billion (related to front-office salaries, interest payments, arena leaseholds, facilities, etc.) if the season is canceled.

If there is so much upside to coming to an agreement, and so much downside to canceling games, then why didn't they figure something out?

It turns out this phenomenon is not limited to the NBA, or even to labor negotiations. It also turns out that this outcome was predictable. A branch of mathematics called Game Theory examines conflicts and attempts to model them as simple games. Remember John Nash in "A Beautiful Mind"? Nash received the Nobel Prize for his work in this area. The phrase "zero-sum game" comes from this discipline as well.

Game Theory has applications in economics, evolutionary biology, computer science, social science, politics and psychology, and it can help us understand the NBA labor mess. We can use a game called Prisoner's Dilemma to model the current situation.

Here's the classic example:

Two men are arrested, but the police don't have hard evidence to ensure a conviction. So they separate the two men and offer both a similar deal -- if one testifies against the other and the other remains silent, then he goes free and the other receives a one-year jail sentence. If both remain silent, then they both receive just one month in jail for a minor charge. If they rat each other out, then each receives a three-month sentence. The two prisoners can't talk to each other, and both know that they were offered the same deal.

What do you do as one of the prisoners? Do you aggressively rat out your accomplice? You might go free, or you might get three months in prison. Do you instead stay silent? You might get just one month, but then your partner might rat you out and you'll spend a year behind bars. This game illustrates a situation in which it looks like both parties should agree, but there are reasons why neither party is willing to do so.

That's where we are in the labor strife. It makes perfect sense for the two parties to agree, play out the season and receive substantial monetary rewards. However, that's easier said than done, and the sides seem willing to sacrifice the entire $4 billion in revenue. Both are behaving like the prisoners in the Prisoner's Dilemma.

The game tells us that it is best to take an aggressive position, as being passive can lead to trouble. Both sides want more than 50 percent of the $4 billion, and are both posturing to appear aggressive and non-conciliatory. Whether you're the NBA commissioner, the NBPA president or a prisoner facing a jail sentence, you start this game by looking as tough as possible. You try to scare your opponent into submission.

Phases of the game

The Prisoner's Dilemma takes place once as a single game, but that doesn't exactly reflect the ongoing labor situation. The labor negotiations aren't a single game, just as poker isn't just a single hand -- the way you've played in the past directly influences how your opponent will play against you in the future. What we really have is a series of these games, with the stakes getting higher and higher as time passes.

In the first games (or weeks) of negotiations, nothing was at stake because a wasted week wasn't a big deal -- the regular season would still start on time. Since there was no cost of lost revenue, both the owners and the union used this time to posture aggressively.

That was the first phase. We are now entering the second phase. From this point forward, every lost opportunity to settle will result in lost regular-season revenue. Posturing instead of cooperating will now have great financial repercussions on both parties.

The two sides are fighting over 3 percentage points of that $4 billion pie. Over six years that's approximately $720 million -- a hefty sum that dwarfs two weeks' income, making those additional percentage points seem like a worthwhile gamble. Over a longer term it looks insane, which is why it makes perfect sense to settle now rather than wait until January 2012. Yet that isn't likely to happen.

We also have to remember that a complex negotiation can't be reduced to a simple math equation. There are numerous other factors involved, such as egos, strategic positioning for future negotiations, and give-or-take on system issues. But the revenue split is the big piece. Solve that, and the rest will fall into place.

Stakes of the game

The NBA owners appear anxious to test the resolve (and bank accounts) of the union members as they firmly believe they'll win in a waiting game. But at some point the stakes for the owners will increase dramatically because of the loss of games that should have been part of the national TV schedule. Then, sometime in January, the expenses for both sides will skyrocket to $2 billion, as they face cancellation of the entire season. There will be no paychecks for the union members, and little basketball-related income for the owners.

That's when we enter the end game of the Prisoner's Dilemma. This will feature both sides alternatively threatening catastrophic effects for the other side, while simultaneously sending out signals that they want to reconcile -- like John F. Kennedy dealt with Nikita Khrushchev during the Cuban missile crisis. Both sides will threaten to end the season while simultaneously finding ways to back down and accommodate the needs of the other side. Using the Prisoner's Dilemma as a model, the two sides will both step back and take a passive stance in order to salvage the season.

Does it really have to come to this? Probably. The cost of one or two weeks' lost revenue isn't enough to alter the course of the negotiations. Each lost week or two of games becomes a sunk cost -- if you're negotiating over whether to start play during Week 8 of the regular season, it makes no difference that both of you have already squandered seven weeks of revenue. But as the entire season is threatened, the potential cost overwhelms that of one or two weeks' lost revenue. The nearer they come to the point of no return, the more they will have to factor this prospect into their decisions.

If the potential for a lost season isn't bad enough, there is more at stake if the two sides cannot come to an agreement in early 2012 -- if the season is canceled, the players will likely decertify the union. If that happens, the ultimate war in court could cost the 2012-13 season, and possibly the 2013-14 season as well. It could also result in treble damages for the owners (up to $6 billion per season) should the players prevail.

Players of the game

Is there a better solution? While the numbers beg for conciliation, the games played internally among the owners and the union members preclude an easy answer. Both the union and the league are comprised of many individuals, and the members of both groups have different motivations based on what they earn, what they have saved, and what they are willing to risk. In other words, both the league and the union have strong internal factions.

These factions influence the negotiations in two important ways. First, both the owners and the union members can pass a labor agreement with a simple majority vote. For the owners, this means "hawks" who favor a hard-line stance want to convince the middle-class owners that the risk of lost games is worth holding out for a larger share of the pie. Conversely, the "doves" want to persuade the middle class that it is better to start the season, as the losses will start to take a huge toll on their finances.

Among the players, the union members with the highest salaries have the highest savings and the longest careers. Conversely, the lowest-paid players have the shortest career shelf-lives and likely less money saved compared to their elite brethren. They have the most to lose in a prolonged labor lockout -- and yet the elite union members have much greater influence over the process than their lower-paid colleagues.

The second important attribute of these factions is the potential to "divide and conquer." Both the owners and the union have attempted to present a united front, as dividing according to their self-interests would undermine the negotiation. This is reminiscent of a scene from "The Godfather," in which Don Corleone admonishes his son to never tell anyone outside the family what he is thinking.

Weakness is not the same as cooperation in the Prisoner's Dilemma -- it means you have no better recourse than to capitulate. Cooperation means you are willing to discuss a solution that might bring your opponent closer to a mutually acceptable resolution.

From what we've witnessed to date, factions within the ownership group (the hawks) and union members (the elite players) appear to be an impediment to an early resolution.

What can be done now?

Last week, David Stern approached the players with the idea of a 50-50 BRI split, and though the owners never voted to ratify that offer, you have to assume that Stern is very confident that he can sell it. It also was never put to vote by the players, as a few of the elite union members rejected it outright, holding firm at 53 percent.

The two sides should agree to hold separate secret votes among the franchise owners and union members on whether to accept 50 percent, after being shown the penalty of waiting week to week. The voting should be administered by a trusted intermediary not connected with either side who keeps the individual votes secret. If at least half the voters on both sides votes "yes," then the result becomes official and binding.

The secret vote removes the barriers to factionalism among the owners and union members, preventing the Prisoner's Dilemma from spiraling out of control until early 2012. A simple vote can therefore save nearly $1.5 billion and will likely reach a similar conclusion to what the two sides will eventually agree to after the new year.

Another possibility lies in bringing in an outside agent that can steer the game from its current course. Union executive director Billy Hunter said Wednesday that the two sides will meet with a federal mediator next week. It remains questionable whether a mediator would be able to persuade either side to step across the line in the sand they have already drawn -- the Prisoner's Dilemma model explains why the sides are not inclined to deal right now. However, a mediator could help neutralize the internal factions and bring the two sides closer to an agreement.

Incomprehensible as it would appear at first glance, the two sides in the labor dispute are behaving according to what the Prisoner's Dilemma model would predict. The only question remaining is whether they will play this game out to its conclusion, or realize that even if one side wins, they both lose.

Author's note: Edward Gleason, a Boston-area CPA who holds an MBA from Yale and is one of my advisers on economic issues related to the labor dispute, contributed greatly to this article.

Larry Coon is the author of the NBA Salary Cap FAQ. Follow him on Twitter.