I learned some game theory while I was a graduate student. At the time it seemed like the answer. It took strategic thinking seriously and appeared to make sharp predictions about equilibrium outcomes. Deterrence in the nuclear arena may have been its crowning achievement. MAD worked.
I started to become disenchanted with game theory ten to fifteen years later, after learning about the Folk Theorem of infinitely repeated games which says, more or less, that any individually rational outcome can be an equilibrium - so much for sharp predictions. Like general equilibrium theory before it, which produced similar results about what could be an equilibrium outcome, game theory itself had little to say about what we might observe, especially if we wanted to otherwise be general in the formulation. The sharp predictions were a consequence of ad hoc assumptions made about the structural form of the game.
The last decade or so there seems to be a new phenomenon to upset the strategic apple cart, though I'd be happy to be corrected by folks who better understand history than I do that it is more a rehash of the megalomania of the fascists from the 1930s coupled with the utter paranoia of the Joe McCarthy years. This is the rejection of rationality itself, at least in public posture, by leaders who claim to be on a divine mission.
The first instance of this that we observed could be found in the utterances of President Mahmoud Ahmadinejad of Iran on the topics of Israel, The Holocaust, and Iran's plans for developing a nuclear capability. The guy may have been rational in fact, but he came across to many people, myself included, as completely crazy - what he was doing didn't seem to be in Iran's own interest, even if you take the point of view of the iron-handed leadership of that country. His successor is demonstrating that now by backing away from those positions.
Before I get to talking about the current situation with the Tea Party, let me talk a little about what economic theory should be good for, which is to think forward strategically, figure out what equilibrium looks like in the future, and then reason by backward induction about how that should impact present thinking and action. So, with the debt ceiling debacle we are currently in, we might consider what the world will look like one month from now, which happens to be Election Day, though it is an off year for elections for national office.
In this simple analysis there are three possible states that might be reached: (1) there is no agreement on the debt ceiling and the country ends up in default, (2) there is an agreement where a clean CR is passed, and (3) there is an agreement with some concessions about spending cuts added in. It is important to note, if you are doing a game theory analysis, that we are already in the subgame where it was possible to avoid government shutdown by the passing of a clean CR, but that alternative was scrapped.
Alternative (1) is not just that all players lose, it is an unmitigated disaster that might very well cause a world-wide depression. Alternative (2) would be a reasonable outcome economically, but it clearly would reduce the cachet of the Tea Party radicals in the House and/or it would result in John Boehner's ouster as Speaker, and it would result in a divided Republican party in the House. It is therefore not a situation that rational Republican players would have desired at the outset. If a clean CR had been passed before the shutdown, there would not have been the loss of cachet for the Tea Party. Alternative (3) would be worse economically than alternative (2) but certainly better than alternative (1), but it would be horrible for the Democrats and President Obama, because it would reward hostage taking as a strategy by the Tea Party Republicans.
Now add to this that Speaker Boehner has said publicly that he won't allow the country to default and all he has to do is bring the Senate Bill to the House floor for a vote to achieve outcome (2). That now appears to be the likely equilibrium, with Speaker Boehner falling on his sword. But if that's right, it makes what the Tea Party radicals have done seem irrational. They will have played out the hand and lost, when they could have folded earlier and kept their stash. If this outcome does indeed happen, and several days before the date when default would occur, it will make it appear that the Tea Party types severely miscalculated. Rational players don't do that.
Let's turn to the decision making from Speaker Boehner's position. He may still wish to hold onto his position as Speaker, so could delay his bringing the Senate Bill to the House floor, in the hope of getting both Harry Reid and President Obama to bargain, where neither has indicated any willingness to do so to date. But, it would seem, eventually the Speaker must bring the Senate Bill to the floor if he doesn't otherwise extract concessions. Understanding that, neither Harry Reid nor President Obama have incentive to compromise one inch. Thus, in any equilibrium situation Speaker Boehner brings the Senate Bill to the House floor. The only question is when. And if even in delay he gets voted out as Speaker because outcome (2) was produced, then his incentive for delay is weak.
So we seem to be on a branch of the game tree that we should not have reached and having gotten this far, it would still seem that outcome (2) is the only possible equilibrium play. That the Tea Party members of Congress appear to believe otherwise makes this seem more like a rehash of the Three Little Pigs, with them in the role of the Big Bad Wolf, yet hoping for a rewrite of the story's ending.
Public posture that seems irrational may make perfect sense as a tactical ploy, but interpreting what the Tea Party radicals in the House are doing as rational makes sense only if the threat of (1) happening becomes real for the Democratic Leadership. That is reliance on an out-of-equilibrium threat to win the day. It is a strange way to play the game.
If outcome (2) does happen then one might ask: what is the impact on future elections as a consequence? It is hard to see this persuading Independents to vote Republican.
There is perhaps a different way to make sense of what is happening from the Tea Party side of the equation - using an analogy with a wounded predator. Such a predator fights very aggressively because survival is threatened. Many commentators have written that the demographics are all wrong for the Republicans in the future, unless they significantly change their message. In other words, if the options are either a slow death or a rapid one, then continuing the fight to the bitter end can make sense. But that in itself doesn't produce concessions from the Democratic leadership. Indeed, it might very well have the reverse effect than intended and strengthen the Democratic hand.
In reading the news about the issues, it is very hard to trust what people are quoted as saying, not the words themselves but whether the words represent what they actually think.
Given the above analysis, my prediction is that there is a clean CR brought to the House floor by this Friday. It will pass. Then all hell breaks loose among the Republicans in Congress. That's what happens when you you overplay your cards.