Legislative Game Theory

We were studying game theory in econ this week, but it was all stuff I already knew, so I spent that time concocting game theoretic representations of various events from the recent past and near future in American politics. Let's start with the Bush tax cuts debate of last December, and also of next winter as well. Let's imagine that there are two players, both with absolute veto power, called Obama and Boehner (McConnell was the veto player last year, but Boehner will be next year and is more prominent anyway). Obama proposes an extension of the tax cuts for those making under $250,000 per year. Let's say that Boehner proposes an extension of tax cuts for those making over $250,000 per year; really he would be proposing tax cuts for all, but it's a lot easier to see the game this way.

There are four possibilities for outcomes here. If both players agree to the others' proposals, then everyone gets a tax cuts. If only Obama vetoes, then poor people (relatively speaking) get a tax cut. If only Boehner vetoes, then rich people get a tax cut. If both players veto, no one gets a tax cut. So what are the two players' preferences? Boehner, I think, is like this: cuts for the rich > cuts for all > cuts for the poor > cuts for none. Obama, in late 2010, was like this: cuts for the poor > cuts for all > cuts for none > cuts for the rich. (Strictly speaking Boehner's irrational, since he prefers adding cuts for the poor only if there aren't also cuts for the rich, but whatever.) So we can construct the following little Punnett Square of possibilities:

If we assume that the decisions are both made without knowledge of the other's decisions, and that no communication is allowed, then obviously Obama should veto, since he gets a better result in either case that way, and Boehner should therefore cooperate since he prefers cutting taxes for somebody, even if it's poor or working-class people, to cutting no one's taxes. But those assumptions are obviously wrong. Instead let's assume that Obama has to go first, in a sense, by both proposing certain pieces of legislation (since the Democrats control both Houses, he gets to do this) and by signalling what he will or won't veto. Then, once Obama sets those parameters, Boehner makes his decision, and then Obama is bound to obey the rules he set for himself in his original move. Both are allowed to communicate with each other before the decision. Now, Boehner clearly can't get his optimal position, because it's Obama's least favorite position and Obama will do anything to avoid it. But suppose Boehner says before the game starts, "look, I'll agree to your tax cuts only if you make it clear that you'll agree to my tax cuts, too." Then for Obama to try and veto Boehner's cuts would get him no cuts, which he doesn't want. So he will propose a full tax cuts package, but make clear that he'll veto a tax cuts for the rich only bill if it gets to him. Then Boehner agrees to this, and we get tax cuts for all. That's approximately what happened, except that the concept of extending the cuts for just the rich were never on the table.

Now let's see what might happen in late 2012. There's only one key thing that might have changed: if the economy is significantly better in 2012 than it was in 2010, Obama might be able to credibly prefer cutting no one's taxes to cutting everyone's taxes. And that changes the game rather dramatically.

Now John Boehner has a problem, which is that Obama prefers either outcome in which he has issued a veto to either outcome in which he agrees to Boehner's tax cuts. That means Obama has a dominant strategy, which means he will pursue it. So Obama is going to propose tax cuts for the poor only, and if Boehner votes them down, so be it. But in this situation, Boehner has no incentive to vote them down. There's nothing he can do. There's no threat he can make that will get Obama to be even remotely flexible. Also, an election will have just happened, probably one in which Obama got re-elected, so the optics of cooperation won't be horrible. If Obama is able to commit to preferring cutting no one's taxes to cutting everyone's taxes, he can win this game when we play it a second time. That, by the way, is why the tax deal was always a better bet than some people seemed to assume.

But let's talk about what's going on now, namely the game of brinksmanship over the budget. Same players, with the following possible outcomes: if both players cooperate, we get modest spending cuts; if only Boehner vetoes, we get drastic spending cuts; if only Obama vetoes, we get no spending cuts; if both players veto, we get a government shutdown. (Note, "veto" is really sort of the equivalent of "hold firm," not explicitly a veto. But you get the point.) Democrats want as little cutting as possible, Republicans want as much cutting as possible. But how do they feel about a shutdown? Let's assume that the Republicans are proposing cuts that are just too damn far for the Democrats to take, even if it means a shutdown, and let's also assume that Republicans, some of whom would actually take a shutdown as a first choice, prefer it to a modest cuts package. (We can tinker with that later on.) Here's what that looks like:

Vetoing is a dominant strategy for Boehner. Therefore, there's nothing Obama can do to talk him down from a veto. Which means Obama ought to veto as well. Which means shutdown. To put this game in somewhat less discrete terms, since the budget is a more or less continuous thing in terms of total spending, Obama and Boehner both propose a level of spending cuts. We then suppose that there is a level of cuts above which Obama prefers a shutdown, and a level of cuts below which Boehner prefers a shutdown. If the Boehner level is lower than the Obama level, then in theory there's an optimum range where they're both okay with the result. If not, we're heading for a shutdown, and there's nothing we can do about it. And it's gonna suck.