## The Extortion Game

I always enjoy reading Eric McErlain’s thoughts over at Off Wing Opinion, and something he said the other day got me to thinking.

…Washington is simply more valuable to MLB without a team, as a bargaining chip to blackmail other cities into paying for publicly funded stadiums, than it is as a home for the wayward Montreal Expos.

I have heard this explanation for the lack baseball in DC many times, but I am not sure if the explanation holds water. (BTW, do not take this to be an indictment of Eric’s site, he just got me thinking. Off Wing is one of the best sports weblogs on the web. If you are not reading it daily, you should be. Eric does a fantastic job.) While MLB might gain subsidies for threats to leave to DC, MLB is certainly losing something, the revenues of having a baseball team in DC. The question is, do the revenues generated by the extortion threat exceed the revenues lost from not having a team in DC? Let me set up a bare bones model to see what is necessary for extortion to work.

When there is an available market for a MLB team the league has two options:

1) sell an expansion team to the new market or

2) use the market to extract subsidies for current teams in the league.

The expansion team will sell for the net present value of the future revenues of the team (V) and be divided equally among all (N) teams. Thus each team will receive V/N from the expansion team. When extracting subsidies the amount any team can extract is equal to the probability (P) that the team will leave for the open market multiplied by V. Since only one team could move to the target market, the probability that a team will leave will be 1/the number of marginal teams threatening to move (M), or 1/M. For example, if ten teams threaten to leave for DC the probability than any team relocates is 0.1. Therefore, the total amount of subsidies each marginal team can extract is equal to V/M, with a total value that will sum to V for the entire league.

If every team in the league can threaten to leave its current city then the owners will receive subsidies equal to the gains from expanding to the new market. However, there is a problem with this. Expansion threats by existing teams must be credible. The Yankees and Red Sox may get public subsidies but no politician would seriously believe these teams would move to another market. Teams that cannot credibly threaten to leave a market receive none of the benefits of extortion, while M teams will receive more subsidies and prefer extortion to expansion.

So now we get down to the nitty-gritty. The current MLB rule is complicated, requiring ¾ of the affected league and a simple majority in the other league for approval of relocation and expansion. Basically, this means the league needs 20 teams to approve either relocation or expansion. Let’s assume all M teams would vote for relocation (because it makes their threats to leave credible) and all non-M teams vote would vote for expansion. If the number of M teams were greater than 19, the league would choose to use an available market for extortion rather than expansion. Twenty teams could credibly threaten to move to the new market with each receiving 1/20th of the value of hosting a new team in the target market. If the number of non-M teams were greater than 19, then the league would choose to expand into the new market with each team receiving 1/30th of the value of the new team. But we have some indeterminate space. What happens if neither faction has the required supermajority? Well it depends on bargaining strength, and I think the non-M teams will have a stronger position. Why? The status quo, with no team receiving any fraction of V, is the fallback position. M teams have something to gain from V (V/30), but non-M teams do not receive anything from relocation. No non-M teams would have an incentive to deviate from the status quo, but M teams do have reason to deviate. So what does this mean? Well, the choice of expansion versus extortion is determined by number of M teams.

Likelihood of reality about the number of M-teams:
–10 or less: Most realistic (like at Radio Shack)
— Less than 20 but greater than 10: Possibly realistic
— 20 or greater: Not realistic

This leads me to believe that MLB is more likely to use available market for expansion rather than extortion. Now, before you start flaming me for all of these “assumptions” I will grant that the model is very basic. It is just a starting point for my thinking on this issue. I am happy to receive suggestions. I think the most troubling unstated assumption of my analysis is that cities with teams properly perceive the threat of a team leaving. If the probability of departure is perceived to be greater than the actual probability, then extortion may be preferable to expansion. But, if cities overestimate the probability of team relocation, then leaving a city open for extortion is not necessary. Owners can extract subsidies by threatening to move the team to unqualified markets AND obtain revenues from expanding into a qualified market.