Hurtling Towards A Cliff

Hurtling Towards A Cliff « Cheap Talk

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.

This is a competitive situation in Aperiomics with Iv-B and Oy-R, often as people race to a boom or bust those who chicken out lose. For example R prey might have to grab all the food they can and keep having offspring to survive, those that don't get eaten more by Oy predators in a drought. Oy might try to grab a crocodile's eggs before it can get to them, in a drought the ones who chicken out more die more than those that get caught by the croc.

In an Iv-B boom those that keep investing need to make every profit they can to survive the bust better, it is like trying to run towards a cliff grabbing food or money with a mob. The idea is to grab all they can and then reverse direction without the mob behind pushing you off as they grab things. For example in a sale people at the front have to balance getting a bargain and getting crushed as the doors open. People exiting a burning theatre have to balance getting out first or getting crushed by the others.

This then is why in a boom it accelerates towards the ceiling and a crash and then to the floor and another crash, also there is bluffing like in chicken where people need to make others get more hurt otherwise others will do it them worse.

It is also where tit for tat doesn't work, people are better off grabbing food or money near the cliff edge than waiting to make a deal with others.

In equilibrium of this game, unless someone concedes right away there isnecessarily 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.