Wireless carriers and the regulatory game tree

AT&T wants to buy T-Mobile. In the US, such a deal requires the permission of the FCC and the DOJ. The purpose of such regulatory approval is ostensibly to limit any restraint of trade that may arise from greater concentration of the industry.

Some simple models of market power (say, a Cournot model) assume that greater concentration in an industry means higher prices for consumers. Others, like Bertrand models, predict no change in prices. More complex models that account for fixed costs and increasing returns to scale may even predict lower prices for consumers, i.e., price competition is Bertrand, but marginal cost is decreasing over the relevant scale. There may be other factors that the government may look at in terms of whether to approve the merger, but they generally will correlate with consumer prices.

So how can we know which of these models applies to competition in the wireless industry? One piece of evidence to look at is whether other carriers support or oppose the merger. If Sprint and Verizon support the merger, then that suggests that they believe that basically a Cournot model applies. If they are indifferent, they think the merger will not really affect their pricing ability. If they strongly oppose the merger, they think prices will fall due to factors such as increasing returns to scale.

According to Reuters, Sprint has announced that they are opposed to the merger. On the face of it, this suggests that they expect consumer prices to fall. The government can use this information as evidence of increasing consumer welfare from the merger; they may therefore be more likely to approve the merger.

Nevertheless, the game theorist in me can’t help but take a walk down the game tree. Sprint knows that any information that they reveal to the Feds may affect the outcome. Therefore, a shrewd Sprint will publicly oppose the merger if they privately support it, and vice versa. Do the FCC and DOJ realize this? Maybe, in which case you would expect Sprint to take the opposite tack, and so on. The bottom line is that if all players are rational you can’t read much into whether the other carriers support or oppose the merger as some economists suggest. And of course if your model of the FCC and DOJ is that they are composed of non-economists who don’t understand much of this, then your interpretation of Sprint’s actions hinges on exactly how much of the game tree the Feds can see.

By the way, Sprint’s stock fell by 15 percent around the announcement of the proposed merger, which suggests (barring complicated equilibria) that they are telling the truth. Which further suggests that they think the regulators are stupid.