As budget negotiations get underway with the threat of sequestration looming, it’s worth recalling a basic lesson from game theory.

Consider two parties in the same vehicle speeding towards a cliff. The one who concedes, i.e. chickens out and steers the car out of danger, is the loser. Winning is better than losing but either is better than driving off the cliff. Finally, time is valuable: if you are going to concede, you prefer to do it earlier rather than later. Still you are prepared to wait if you expect your rival will concede first.

In equilibrium of this game, unless someone concedes right away there is necessarily a positive probability that they will go over the cliff.

The proof is simple.  Consider player 1 and suppose his strategy is not to concede immediately. Then we will show 1′s strategy is such that if 2 never concedes there is a positive probability that 1 will also never concede and they will drive off the cliff together. To prove it, suppose the contrary: that 1′s strategy will eventually concede with probability 1 (if 2 doesn’t concede first).  If that is 1′s strategy then 2′s best reply is to wait for 1 to concede. In equilibrium 2 will play such a strategy and the outcome will therefore be that 1 is the loser with probability 1. But if 1 is going to be the loser for sure anyway he should have conceded immediately. That’s a contradiction. We have shown that if 1 does not concede immediately then his strategy will allow the car to drive off the cliff with positive probability. The exact same argument applies to 2. Thus in equilibrium, if the game begins without an immediate concession there is a positive probability they will plunge from the cliff.