Game theory, for all of its hype, isn’t all that great at telling us what to do in real life. When Morgenstern and von Neumann originally published the magnus opus of game theory, Theory of Games and Economic Behavior, one buyer falsely got his hopes up in believing that it might help him manipulate the stock market. Others expressed scorn at the field’s shortcomings and distance from application – game theory could conveniently prove already intuitive results, but it couldn’t tell us how to win at chess.
Despite the fact that game theory is not a panacea for the world’s economic problems, it can still be extremely useful. The telecom auction in the 1990’s, designed by game theorists, saved the US and UK public billions of dollars (a cumulated 35 billion, to be exact). The powerful notion of a Nash equilibrium in multiplayer-games helps break out of the self-referential “I think that-my opponent thinks that-I think that-my opponent thinks that …” infinite loop and identify natural strategies in non-cooperative games.
However, there are many two-player games in which the Nash equilibrium is not a useful concept, because a particular game might have two of them. The famous example is prisoner’s dilemma (read more here: http://plato.stanford.edu/entries/prisoner-dilemma/). Another example is highway chicken:
Two cars face each other at opposite ends of a parking lot, a white line at their midpoint. Both cars accelerate towards each other, presumably at the exact same rate. The player who swerves first before the white line loses, and is deemed “chicken.” If both swerve, the game ends in a tie. But if neither player swerves, they crash, killing each other and destroying their vehicles in the process.
For easier visualization, the payoff matrix is displayed below:
Although originally conceived of in a slightly different form as a Hollywood plot device for getting rid of characters in the movie (Rebel without a Cause, starring James Dean), the game is surprisingly applicable to the real world. Logician Bertrand Russell originally likened it to the Cuban missile crisis – both the USA and USSR threatening each other with nuclear buildup. Whoever backed down first would lose their all-important power in international diplomacy. If both backed down, the stalemate would continue, and perhaps an arms limitation treaty could be reached. If neither did, the result would be a nuclear holocaust – a very real possibility back in October 1963. Russell wrote that
As played by irresponsible boys, the game is considered decadent and immoral, though only the lives of the players are risked. But when the game is played by eminent statesmen, who risk not only their own lives but those of many hundreds of millions of human beings, it is thought on both sides that the statesmen on one side are displaying a high degree of wisdom and courage, and only the statesmen on the other side are reprehensible. This, of course, is absurd…
We now face a surprisingly similar crisis in American politics – namely, the budget crisis and the debt limit. With party-line votes, domination of Congress has mostly degenerated into a two-player game. Democrats and Republicans are pushing their budget proposals from opposite ends of the political spectrum, both extremely reluctant to give up any ground. Technically, the Democrats have the upper hand with a Senate majority and the White House, but the Republicans have a much powerful majority in the House and can effectively get anything through (although it may get vetoed by President Obama or be shot down in the Senate (through which practically nothing gets through nowadays)).
Effectively, the stakes are high and they strongly resemble those of the game of “chicken.” The winner, whichever side holds its ground while the other gives in, would be able to publish and further their political agenda in one of the most important pieces of fiscal legislation in the near future. The case of both sides “swerving” would be a compromise somewhere in the middle. This was already seen with the budget bill passed in early April – Republicans wanted 60 billion in cuts, Democrats wanted none. The figure came out around 38 billion. An interesting case, of course, is the case in which no bill is past because of a gridlocked Congress. The short-term results of possible government shut-down and the longer-term results of drastically reduced political popularity and crushing debt.
The shut-down, of course, is a separate game in itself. There is the interesting case study of the 95-96 government shut-down, although that holds its place in some other article.
So, back to the game. Technically, there really is no solution. There is no strategy that you can point to which will effectively give you the other hand, at least mathematically. On the other hand, if you were lined up to threaten to crash your car into someone else’s, what could you possibly do to make them swerve first?
How about feigning disinterest and acting suicidal?
How about taking a swig of Jack Daniels, putting on dark glasses, blasting music, and revving up the engine? You value your own life, probably equally as much as your opponent does theirs. But if you can convince them that you would be willing to take greater risks and convince them that you would effectively put a lower value on your own survival, then you change the pay-off matrix, and effectively change the nature of the game. All of a sudden, driving straight on doesn’t seem like it’s worth it for the opponent, since they don’t really have much of a possibility of avoiding a crash, and they, of course, value their life more than some stupid game, right?
And they swerve. And they lose. And you, for all your recklessness and insanity, emerge victorious and unscathed.
John F. Kennedy won the Cuban Missile Crisis by calling Nikita Khrushchev’s bluff. As Russell correctly predicted, “you can’t threaten unless you’re prepared to have your bluff called.” The USSR didn’t really have greater nuclear capabilities than the US. With the exception of some early Space Race victories, the USSR didn’t really have a technological advantage of any kind. In fact, they were quite behind. Khrushchev brought out his crazy and suicidal, but he was ultimately matched by Kennedy, who applied strong pressure to make the Soviets back down (It wasn’t that one-sided. For example, the US ended up having to withdraw missiles from Turkey, which was basically the equivalent situation in the Eastern Hemisphere. Or maybe the fact that they were already there is a testament to the US’ dominance).
So what are the lessons for today’s politicians at this point? The Republican Party certainly brings out the “crazy and suicidal.” So far, they have pledged for any amount that the debt is raised by to be matched in spending cuts, which could be in the trillions (for reference, the total US budget is about 3.5 trillion and the proposed cuts would be around 2 trillion). The party took an ideological swing to the right during the 2010 midterms and with the flourishing of the Tea Party movement. Meanwhile, the Democrats have been all but, with Obama compromising on many issues he formerly considered priorities and with two mostly ineffectual years of controlling Congress with a near Democratic supermajority. In order to push their agenda, Democrats would have to take a much more radical and uncompromising stand from the start, and then slowly move along with the GOP towards the center.
Of course, neither party can threaten the other too much in this case, no matter what GOP freshmen would like you to believe. Both parties want the debt limit raised, so Republican demands of “at least one dollar cut for each dollar the debt limit is raised” is, to a large extent, a bluff. Democrats have a technical upper hand by controlling the Senate and the White House, but Republicans have been far less compromising and have wielded control of the House of Representatives with considerable success. So who will win this legislative game of chicken? Rationality has no place here. And Treasury Secretary Timothy Geithner has “11 weeks of legal tricks” to keep the debt below the limit. So just press down on the accelerator and (pretend like you) don’t care.
NB. Another version of the game, which was actually in Rebel Without a Cause,was where the kids accelerate towards the edge of a cliff with stolen cars and whoever reaches the fastest speed before swerving wins. It’s a slightly different premise but the payoff matrix is the same. And the version presented here is a more apt metaphor for human conflict, at least in Russell’s opinion (and I’m inclined to agree).