Here’s a practical application of the bargaining networks that we’ve been discussing recently, and it touches back on the stock market lectures. This article in the New York Times, “When Unequals Try to Merge as Equals“, is about the upcoming (pending approval) merger of the Sirius and XM satellite radio companies. The crux of the article is that while the companies are merging as equals, in reality on the stock market Sirius is worth almost $1 billion more than XM. As a result, Sirius is paying what amounts to a 30% premium for XM shares, so that the merged company will be equally owned by both groups of shareholders. This is somewhat confusing for outsiders, because it’s unclear why Sirius would be interested in such a deal. The author, Andrew Ross Sorkin, explains that the merger made sense for both companies for a few reasons.

Some of the reasons that Mr. Sorkin cites are less related to our course than others. One reason is that a merger of equals is more likely to be approved by the government. Because Sirius and XM are the only two satellite radio companies around, a merger might be a violation of anti-trust, and a takeover of one company by the other might look too much like a monopoly in the making. Another line of reasoning is that, while Sirius is valued more than XM, it is not really worth more: XM has more subscribers and more revenue, but Sirius’s stock price had been inflated because of good press and big deals (such as signing Howard Stern).

The other reasons can be seen as a natural outcome of network exchange theory. As mentioned, Sirius and XM are the only two companies in satellite radio. We can think of them as being the only two members of a graph on these companies. More specifically, we can consider a graph where the nodes are companies and the edges represent mergers. The values on the edges reflect the percentage stake that each company has in the final, merged company. With this model it becomes clear that an equal merger is likely, because while Sirius is the one making the offer, it only has one company it can merge with. While Sirius might be thought to have an advantage because it has more money to spend, in reality it needs XM just as much as XM needs it. As Mr. Sorkin puts it:

And then Mr. Parsons [XM’s chairman] played his ace: If Mr. Karmazin [Sirius’s CEO] wanted to create the enormous savings they both projected would result from a deal — worth more than $5 billion, more than the value of either company — they needed each other. And Mr. Parsons would not play unless his shareholders could capture half of those savings.

This is a classic example of someone playing the Ultimatum Game. Both Sirius and XM need the savings of the merger — they are both losing money — but even though XM is worse off, it refuses to be taken over. Mr. Parsons is apparently a particularly stubborn player of the Ultimatum Game, and in this case Mr. Karmazin was lenient, because he did not try to push his advantage, perhaps because of the other factors in play. Or maybe he just knew how to play the game.