Yankees, A-Rod, and Game Theory

In this Sunday’s NY Times, Jeffrey Gordon pens a Keeping Score column on the bargaining game played by the NY Yankees and Alex Rodriguez. Gordon argues that the Yankees stated refusal to sign Alex Rodriguez upon opting out of his contract is not credible.

Conventional wisdom is that Rodriguez willfully ignored the Yankees’ repeated public assertions that they could not rationally pursue him in free agency because they would lose $30 million from the Texas Rangers when they took over his contract. But the Yankees’ assertion is simply a bargaining gambit.

Assume some other team, call them the Dodgers, were to offer Rodriguez $32 million a year for eight years. Remember that the Dodgers are receiving no part of the Rangers’ booty. Is it really the Yankees’ position that Rodriguez is worth more to the Dodgers than to the Yankees? If the Dodgers can afford to pay the $32 million a year, can the Yankees — the richest franchise in sports — plead poverty?

The Yankees’ earlier protestation about the Rangers’ money was to make it appear their hands were tied, so that they could land Rodriguez at a lower cost. But that bluff has been called. The lost Rangers money merely puts them on the same ground as other teams. How far will the Yankees go with cries of wounded pride?

He’s right on this point. If Rodriguez is worth more to the Yankees than any other team, then the rational choice would be for the Yankees to sign him, even though the Rangers are no longer helping out the Yankees. However, there is more than pride involved. This isn’t a one-shot game, and there is more at stake than one free agent.

The Yankees were in a nice position, their signing of A-Rod would have been partially subsidized by the Texas Rangers. All parties knew that if Rodriguez opted out, the Yankees would lose that money. Both the Yankees and A-Rod’s agent (Scott Boras) have decent estimates of what his services are worth. In ten days they easily could have reached a deal approximating the free agent market outcome, which would have allowed A-Rod to get his money and keep the Rangers on the hook for the rest of the salary. This is why the Yankee’s drew a line in the sand, and Rodriguez knew not to step over if he wanted to stay in New York.

A-Rod won’t wear the pinstripes again. I am certain that the Yankee’s are out of the bidding, even though the Yankees might still value his services more than any team in baseball. What is at stake here is not a single player’s contract, but the organization’s long-run credibility at keeping its word. If the Yankees cave, the repercussions will echo into the future. Why would any player ever not opt out of his deal in the future if he knows the Yankees will give in? Not following up on your threats is bad for your reputation as a tough guy.

This is a game that I play with my daughter all the time—except the stakes are a little different—“if you wake your sister up from her nap, then you won’t get to go to the birthday party.” My life will certainly be more difficult if I had to stay home with two crying girls than if I took one to the party (especially if they serve beer) and left the baby at home with my wife. So, my daughter thinks I won’t keep my word, and she pulls out her tambourine to lead the princess doll parade. What would happen to my reputation if I took her to the party anyway? Any future threats lose their credibility as my daughter realizes their emptiness and her behavior worsens. Preventing a long-run pattern of disobedience is worth well more than any short-term benefits I gain from giving in.

This is the problem the Yankees face. The long run consequences of reneging in this business are high. Between league rules, tax laws, and big egos a lot of deals get done in this business without ink and paper. This can breed friendships as well as keep potential enemies in check. In this case, the Yankees must stand firm.

5 Responses “Yankees, A-Rod, and Game Theory”

  1. Frank says:

    A key point that the column might (I haven’t read it) have ignored is the luxury tax. ARod may be worth more to the Yankees but he’ll also cost them more b/c of the luxury tax. I don’t recall the tax rate but if it’s 1/3 then paying ARod $30m per year will cost the Yankees $40m per year. This is where the Rangers money becomes important–it would offset some or all of the luxury tax hit for the Yankees.

    I’ve never been to a kid’s birthday party where beer was served (for the parents); there were a couple where it would have been helpful.

  2. Ron says:

    All of this assumes that Yankees management is rational. Given their firing of Joe Torre for only making the playoffs 12 straight years and winning 4 championships and 6 pennants and Hank Steinbrenner running around making absurd statements, that’s a shaky assumption to say the least.

  3. Good points but I still have a feeling things could gravitate toward some face-saving on all sides. It is a measure of the magnitude of A-Rod’s proven potential that this is not a tempest in a teapot but a genuinely big issue. A-Rod will always be a special case because his abilities are so huge. The long term ramification of a Yankee failing to resign him could be compared to the Red Sox dispensing with Ortiz and Ramirez, etc.. Could Joe Girardi and Brian Cashman be in favor of getting A-Rod back? Let’s see how it all shakes down.

  4. MJM says:

    One thing I’ve not seen anyone address is the fact that the Rangers subsidy was a form of surplus that the two sides should have been negotiating on how to share. One also has to keep clear the distinction between value and cost
    Let’s suppose that A-Rod has equal value, V, to both the Yankees and team Z. If team Z pays no luxury tax, then they should be willing to pay up to V per year. The cost to match this offer to the Yankees, with a 30% luxury tax, would be 1.3*V – 7 (assuming that the $21 MM subsidy from the Rangers is spread over three years).
    This set of assumptions puts the break-even valuation for A-Rod at $23 MM. The only way that it makes sense for NYY to pay more is if the value to them is higher than it is to the other clubs vying for his services.

  5. Andrew says:

    The Yankees refusal to negotiate with Rodriguez after he opts out is a classic example of a trigger strategy common in repeated games. Both sides can cooperate and work together, but if one side defects, it results in both sides reaching a different equilibrium for the rest of the games, in this case the Yankees refusing to negotiate in 2007 and likely they will never participate in bidding for Rodriguez ever again. This, of course, is punishment because if Rodriguez is a free agent, his payoff is greater if the Yankees are involved in the bidding than if they are not. It is beneficial for Rodriguez to opt out only if the payoff for defecting in this first game outweighs the punishment payoff for all future games.