With less than a week to go until pitchers and catchers report to spring training, an annual ritual nears its final stages. Players with one year remaining on their contracts and the teams that employ them have been playing out the largely predetermined roles of Blue-footed Boobies in their mating dance. Teams hope to lock up their players beyond the upcoming season at a discounted rate. Players hope to guarantee a certain minimum level of income for the future without giving away too much of the money they could stand to earn on the free-agent market.

In the context of this kabuki theater, how much can we trust what teams, players, and agents have to say publicly about the process? Consider the biggest fish in the contractual backwater this year: Albert Pujols. Set to become a free agent after the 2011 season and reportedly seeking a contract in the ballpark of $300 million, Pujols has thus far been unable to reach a mutually satisfactory deal with the Cardinals. That failure may not seem so stark—after all, the parties have almost an entire year to work out the terms of an extension. Or do they?

Pujols will arrive for spring training on February 16. According to reports, he has instructed his agent—Dan Lozano—not to discuss contract terms with the Cardinals after that date. Thus, if the Cardinals are enthusiastic about getting a deal done, their exclusive window is closing rapidly. After Pujols reports to camp, the Cardinals will have to wait until after the season—when their leverage will have almost entirely disappeared—to rekindle discussions. There is evidence that the parties remain far apart in negotiations, and that the odds of a final deal being in place by the deadline are long indeed. The specter of Pujols in—gasp!—Cubbie blue looms large.

Pujols isn’t the only player to impose this kind of deadline, thereby depriving his team of an untrammeled exclusive negotiating window. Rickie Weeks has also set such a deadline, is also in the last year of his contract, and has also been trying to work out a multi-year deal with his club. But Weeks, unlike Pujols, has at least some semblance of a commitment device to make his threat credible. He and the Brewers have a date with an arbitrator on the 17th of February; if no deal is struck by then, the parties will have their hands forced. Given that the offers exchanged by Weeks ($7.2 million) and the Brewers ($4.85 million) are quite far apart, both parties may have incentives to agree in the next week.

What about la maquina? He says he has a deadline, but is it credible? Sure, you may be thinking. Pujols is a class act, 100% ballplayer. His word is his bond. That all may be true, but what good will it do when tested against the inexorable allure of rational self-interest? In this case, an analogy to a profit-seeking monopoly firm may be instructive.

Imagine a market for widgets in which there is exactly one firm, the monopolist. Because the monopolist sells a unique product, it has market power to charge a price that is higher than that which it could charge in the presence of full competition. This is great for the firm—firms seek profits, and monopolies get profits almost by definition. But it’s bad for the consumer, who has to pay a premium to stay well-stocked with widgets.

One day, an upstart competitor threatens to enter the market for widgets. The widget competitor is jealous of the monopoly’s profits and realizes that if it can get a widget factory up and running, it can make money by charging slightly less than the monopoly—but perhaps still more than the price under conditions of full competition. The competitor likes this idea because even upstart competitors seek profits.

The monopolist, sensing the threat from the competitor, hatches a brilliant and devious plan. Why not, the board asks, carry out a preemptive strike in the price war? The monopolist decides to cut prices even below what it costs to make an individual widget, or in other words, to lose money on a per-widget basis. If it can hold out long enough to keep the competitor out of the market, it can go back to the good old days of pure monopoly profits. And because the monopolist had such a long period of unchallenged dominance, it has amassed a hefty war chest indeed. So the monopolist calls its contacts at the Wall Street Journal and gets them to run a story about how the monopolist plans to slash its price on widgets.

What will the competitor do? Here game theory becomes helpful. If we have only two firms and the payouts are such that the monopolist will be better off profit-wise in the long run by accommodating the competitor (i.e. raising its prices again) than by continuing to keep prices low, it will do so. That is true even if the best outcome for the monopolist is if the competitor never enters. The reason is that entry and accommodation is the equilibrium under these circumstances.

That means, somewhat counterintuitively, that the monopolist cannot credibly commit to keeping prices low in the long term simply by deciding to do so. Instead, the firm must lash itself to the mast somehow. Often, firms can do this by building extra factories or signing big contracts that lock it into a particular level of output (which in turn affects the price it sets).

The question remains whether Albert Pujols has any such commitment device. Without one, it is hard to believe that he will not simply act the monopolist. Imagine that the following hypothetical scenario arises on February 20th, after the supposed deadline has passed. Cardinals GM John Mozeliak calls up Lozano and offers 12 years, $330 million. You are Pujols. What do you do?

You might object that if the Cards were willing to go to 12 years or pay that much money, then why wouldn’t they do so before the deadline? That’s fair enough as far as it goes, but there might be reasons that the Cardinals weren’t prepared to make such an offer until later on. But the larger point remains—Pujols and Lozano would be out of their minds not to accept the deal. So how can they make the deadline seem credible?

One possibility is common in these sorts of statements: the player, bless his soul, doesn’t want the contract situation “to be a distraction.” Play the game and leave the rest of that junk in the clubhouse, as it were. But all that talk would be much more believable if it hadn’t been done before. Last year, Joe Mauer made similar statements before reporting for spring training. A month after showing up in Fort Myers, he was the proud owner of the biggest contract ever given to a catcher.

Another possibility is that Pujols will enforce the deadline now so that it constitutes a credible threat later. In doing so, Pujols could send a message to anyone else who might negotiate with him in the future, suggesting that he will keep his threats. Indeed, Pujols has in the past been consistent about not talking about contracts once spring training has begun. But all indications suggest that this upcoming contract is to be Pujols’ last major deal. He is already in his 30s, and any deal will almost certainly take him close to his age-40 season. So what negotiating reputation could there be left to preserve?

But let’s be charitable. Maybe Pujols takes it to be such an essential part of his integrity that he means what he says, and that to go back on his deadline would cause him tremendous mental pain and anguish. Think of it as a sort of personality-based commitment device. Pujols could have just such a personality.

But it does raise the question—exactly how much money would overcome the pain of self-contradiction? Just ask Joe Mauer.

If all of this is true, the Cardinals, news media, and fans would do well not to place too much emphasis on any artificial deadline, and instead look at what the team is willing to offer and what Pujols is willing to accept. At the very least, the passing of the “deadline” will mean something wonderful has happened—baseball has begun its slow migration northward.