The Matsuzaka Dilemma

From "Play's the Thing," Woodstock Times, December 13, 2006:
This whole swirl may be over by the time you read this, but the meaning is the same, no matter how it comes out, and so is the moral. I’m talking about the sequence in which the Boston Red Sox were revealed to have outbid other baseball clubs for the thirty-day negotiating rights to “posted” Seibu Lion pitcher Daisuke Matsuzaka, who wishes to pitch in the United States but is not, under Nippon Professional Baseball (NPB) regulations, eligible for free agency until 2008. This Thursday night at midnight, when December 14 becomes December 15, is the witching hour.

As I write, Boston Red Sox executives have just landed the owner’s plane on the West Coast to plant themselves on agent Scott Boras’s doorstep. His Japanese client is mum on the seeming breakdown in negotiations, but as he has not fired his representative one may deduce that he is in on the game. It is a game designed by Major League Baseball (MLB) and the NPB, but as they seem only dimly to have understood their own rules, D-Mat and his designated hitter have made their own—or rather, as we shall see, correctly fathomed the implicit rule structure of the posting system. Bottom line: no matter how this shakes out, while D-Mat is not exactly the reincarnation of Curt Flood, Scott Boras has taken the mantle of Marvin Miller, and is my new hero.

Yesterday I had lunch at the local Chinese restaurant where, despite my better judgment, I ate my customary sacramental portion of the stale fortune cookie and read its message. “It is better to have a hen tomorrow than an egg today” was the word from on high. Wait, I thought; this reverses the more commonly expressed wisdom that not only is an egg today better than a hen tomorrow, but also its avian corrolary about birds in hand and those in the bush. I wondered: might Boras have received the same, seemingly counterintuitive message?

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Let’s back up for a moment and see how we got here. In the system by which a player is to be posted, both the team and player must agree on the posting. The team then notifies the NPB Commissioner’s Office that the player will be posted, which then notifies MLB, which notifies all of its teams. The MLB teams then have four days to submit a closed bid for the right to negotiate a contract with the player. If the high bid is accepted by the NPB team holding the player’s rights, the winning MLB team has thirty days to reach an agreement with the player. If the bid is rejected, the player is not “posted.” If the player signs a contract with the MLB team by the end of the signing period, then the NPB team receives the bid money. If the player does not sign a contract with the MLB team by the end of the signing period, the player is returned to the NPB team and the NPB team receives nothing.

Whoever designed this may have had in mind that classic scenario of game theory called the “Prisoner’s Dilemma.” It is a mathematical and psychological game illustrating how rational actions by individuals may not always lead to positive outcomes for either the individuals or the group. The Prisoner’s Dilemma is described neatly in the Stanford Encyclopedia of Philosophy:

“Tanya and Cinque have been arrested for robbing the Hibernia Savings Bank and placed in separate isolation cells. Both care much more about their personal freedom than about the welfare of their accomplice. A clever prosecutor makes the following offer to each. ‘You may choose to confess or remain silent. If you confess and your accomplice remains silent I will drop all charges against you and use your testimony to ensure that your accomplice does serious time. Likewise, if your accomplice confesses while you remain silent, they will go free while you do the time. If you both confess I get two convictions, but I’ll see to it that you both get early parole. If you both remain silent, I’ll have to settle for token sentences on firearms possession charges. If you wish to confess, you must leave a note with the jailer before my return tomorrow morning.’

“The ‘dilemma’ faced by the prisoners here is that, whatever the other does, each is better off confessing than remaining silent. But the outcome obtained when both confess is worse for each than the outcome they would have obtained had both remained silent. A common view is that the puzzle illustrates a conflict between individual and group rationality. A group whose members pursue rational self-interest may all end up worse off than a group whose members act contrary to rational self-interest. More generally, if the payoffs are not assumed to represent self-interest, a group whose members rationally pursue any goals may all meet less success than if they had not rationally pursued their goals individually. Puzzles with this structure were devised and discussed by Merrill Flood and Melvin Dresher in 1950, as part of the Rand Corporation’s investigations into game theory (which Rand pursued because of possible applications to global nuclear strategy).”

So, the underlying scheme of Prisoner’s Dilemma is to have the two prisoners collaborate wittingly or unwittingly against their own interest, with the outcome weighted to benefit the sate as represented by the police and prosecutor. The dilemma resides in the fact that each prisoner has a choice between only two options, but cannot make a good decision without knowing what the other one will do.

I suggest that the posting system was created along these lines to benefit the “state”—each league and each team involved. Think of MLB and Boston as the police and prosecutor in the above scenario, knowing that the salutary actions of Prisoner A (NPB and Seibu) and Prisoner B (Matsuzaka and Boras) are necessary to prevent the mutually assured destruction (M.A.D.) of MLB. That was the prospect some owners envisioned in 1973-74, at the dawn of free agency: that in an auction scenario, dollars would pursue scarce/unique assets in an irrationally exuberant way that would effectively transfer control of the game into the players’ hands. Marvin Miller cleverly assuaged the owners’ fears while assuring high prices for his players’ union by restricting free agency to those with six years’ service in the major leagues; had he opted for universal free agency, as he might have, the flood of talent onto the market each year would have depressed salaries.

The design problem in the Prisoner’s Dilemma game above is that Prisoner Seibu has its deal in hand and is (ostensibly) denied the option of contributing some of its $51.1 million posting fee from Boston toward Prisoner Matsuzaka’s new contract. Indeed, without flexibility the fortunes of Seibu/NPB are more closely tied to the Police/Prosecutor than to Matsuzaka despite the pitcher’s total control over Seibu’s posting windfall. Boston, which stands ready to pay the sum and call it a bargain, instead feels aggrieved because its $51.1 million in expense is counted as nothing by Boras, who is looking to obtain $100 million for a six-year contract, pretty much in line with what his client would fetch in an unrestricted market. Boston had intended to pay out $100 million, all right, but had figured that Boras would give the club credit for half of that for “liberating” his client. No such luck, nor should there have been.

The posting system entices Boston (and other bidding clubs) with the lure of paying for a free agent in a tangential way that would not increase its exposure to luxury tax. The Red Sox are further compensated by considering the payment to Seibu as an inexpensive licensing or entry fee to market their brand vigorously in Japan. Additionally, the exclusivity that came with their winning bid permitted them not only to pursue Matsuzaka, but also to defend against the Yankees landing him.

With its $51.1 million sugarplum, Seibu thought it was being rewarded for having nurtured Matsuzaka’s talent to the point that he was one of the top five pitchers in the world, and for graciously letting him go to America two years before NPB regulations would otherwise allow. In fact Seibu was also being pulled out of a very considerable financial hole, as the posting fee hits up on their bottom line as pure net income ... plus they gain at least $12 million in the amount they would otherwise have had to pay Matsuzaka for 2007 and 2008, the last years of his contract with the Lions.

MLB/Boston is in effect attempting to coerce a “confession” from Prisoner Matsuzaka because he risks embarrassment by returning to pitch for Seibu after 36,000 fans bade him farewell at the Lions’ Stadium, and because Seibu doesn’t want him back at the forfeiture of $63 million it is already counting on.

What did MLB and the 29 teams not in the running for D-Mat’s services gain by the posting system? A presumptive lid on D-Mat’s demands and their escalating effect on pitcher salaries, already heightened by the ineffectual Adam Eaton and the awful Justin Marquis, each of whom received multiyear contracts at about $8 million per. With Matsuzaka wearing carmine hose, MLB will gain a new hero to promote its brand in Japan as well as the USA, just as Ichiro proved a marketing windfall. In fact this posting system is a nostalgic throwback, recreating for owners a glimpse of the paradise they enjoyed prior to free agency, when they owned the market and could say “take it or leave it” to the players. While the posting system may have been born of a genuine wish to protect Japanese baseball and avoid the appearance of American cultural imperialism, it has played out as an exercise in “Who will rule.”

As Boras has evidently surmised, even though MLB and NPB thought they had boxed in Prisoner Matsuzaka, it turned out that he and his client were not locked in behind iron bars but instead, like Br’er Rabbit, had been thrown into a briar patch from which they could easily escape. Boras has recognized that while the game is structured like Prisoner’s Dilemma, counting upon Seibu and his client to act independently in their perceived self-interest to the benefit of Organized Baseball, there is in fact only one prisoner, and without his yielding, there is no palatable outcome.

If MLB and NPB had a game theory for how this would play itself out, it was the wrong one ... styled as Prisoner’s Dilemma but quickly revealing itself to be the “Dollar Auction,” another, even more vicious game, in which each of two contestants seeks to overpay for an asset in order to avoid being the second-place bidder whose money will have been utterly wasted.

In the Dollar Auction someone offers to sell a dollar bill to the highest bidder. The highest bidder will get the dollar, but the second-highest must also pay what he bid yet get nothing in return. Think here of “throwing good money after bad,” of “saving face,” of “having too much invested to cut and run,” of “staying the course.” If you can buy a dollar for a dime, this looks like a good deal. Even as the bidding rises in ten-cent increments to the 50-cent level, it still seems a bargain. At the 70-cent level, one may expect that all but two bidders will have fallen off the chase. When the dollar-mark is reached, the underbidder, rather than accepting defeat, will tend to bid ten cents more so as not to lose 90 cents.

“People escalate their commitment both to justify their earlier bids and to prevent the financial and ego loss of coming in second,” Max H. Bazerman wrote in Psychology Today twenty years ago. “No specific bid is clearly wrong, since it is rational to bid ‘just another 10 cents,’ if the other party is about to quit bidding. But when both parties think this way, an escalatory spiral emerges that is very reminiscent of the Vietnam War and other international and industrial failures in which both competitors get trapped by their previous commitments.”

At first blush the winner in the Matsuzaka Dilemma appeared to be Boston; if the Mets were second, at $13 million less, they felt no ill consequence of their bid. Had the posting system had been a true Dollar Auction, with succesive rounds of bidding, rather than a veiled Prisoner’s Dilemma with closed bids, the price for D-Mat might have gone much higher, as the underbidder would have been highly motivated to stay in the game. But now Boston’s inadvertent partner has been revealed not to be MLB but Seibu, which unlike Boston—which will retain the defensive benefit of its bid—will lose everything, as if it had been the underbidder in a Dollar Auction. And Br’er Boras and D-Mat, if they do not prevail this year, can play again only with more bargaining clout.

--John Thorn