Yesterday, Matt Yglesias treated us to a game theoretic analysis of the recent statements by John Boehner. I think he’s using the wrong model.
By the end of this year, the Bush tax cuts are going to expire. That means an automatic tax increase for everybody. Barack Obama wants to partially offset that tax hike. John Boehner wants to completely offset that tax hike. Yesterday, John Boehner put out a statement which basically says he isn’t willing to compromise much and not at all on the all-important-to-Democrats issue of increasing progressivity.
Matt’s analysis is assuming that this is similar to the Ultimatum Game. In the Ultimatum game, players A and B have to split $100. Player A offers a split (let’s say 90 for player A and 10 for player B) and player B decides whether to take the split or reject the split. If player B accepts, the split goes through (player gets 90, player B get 10), but if player B rejects, nobody gets anything. The stable equilibria is that player A offers $1 for player B and $99 for themselves. Player B is then faced with $1 or $0, they off course pick $1.
That’s why Matt says that the Republicans are being stupid. In his model, Barack Obama has picked a split: a small tax hike. Now, John Boehner has to pick between taking Barack Obama’s offer or rejecting it. A small tax hike or a big one. According to Matt, this is a no-brainer. Take Barack Obama’s offer: a small tax hike. It’s better than a large one. I think this is a bad model of what is going on here.
They instead are playing something like chicken. The traditional game of chicken involves 2 cars and a lot of testosterone-fueled stupidity. The two players drive the cars head-on towards each other. If one swerves while the other doesn’t the one who swerves is the chicken and are ridiculed. If they both swerve, everybody has demonstrated some manhood, but gets to go home. If neither swerve, the cars crash and everybody dies.
This is what is happening here. There is no order of operations. At any point, either Boehner or Obama can swerve by accepting the compromise offered by the other side. But if they don’t, they crash and we all pay higher taxes. (something neither of them wants to see happen for electoral and other reasons)
So now we get to why John Boehner would make such a statement: he’s trying to win. How do you win at chicken? It’s simple, you grab a screwdriver, pull out your steering wheel, and prominently throw it out: you transform the game from Chicken to Ultimatum. Once your steering wheel is removed, the other guy knows you actually can not swerve. You’ve given him the choice: everybody dies or he looks stupid. Obviously, he doesn’t want to die, so he swerves and you win.
In politics however, there is no actual steering wheel. So what John Boehner is trying to do is raise the cost of swerving for his side. He makes statements, his people sign pledges, etc… If they cave, they will look stupid. This all has the same aim: change the payoffs of the game such that swerving for them will be worst than not swerving. They want to setup a situation where they can go to Obama and be able to truthfully say: “Look, we are worst-off agreeing with you than we are just letting the tax hike happen.” Of course, Obama is trying to do the same thing. In the end, they might all swerve. Or not.
What about us, the people? Oh, we lose. Why do you ask?