Sunday, 8 September 2013

Runaway Slaves, Marathons and Economics

In my youth I always fancied myself as the firebrand revolutionary. Although considering I never really played truant, didn’t get into much trouble at school, never did drugs nor even smoked cigarettes I think this was more in my mind than in reality.
Being of Jamaican heritage one revolutionary fantasy that persisted into my twenties though is the idea that if I had lived in the 1700’s or 1800’s I would have been a runaway slave. “I wouldn’t have cut sugar cane or picked cotton for anyone!” or so I used to tell myself. It’s a common enough fantasy of young black men brilliantly illustrated by Eddie Murphy in his seminal 1980's stand-up film “Delirious” (it’s worth a watch before you continue reading)
Now I am in my 40’s, having read economics at university, I thought I would combine my love of running with a little economic theory and revisit the subject of runaway slaves. (Don’t worry people I won’t be writing about “quantative easing” or "interest rate defaults")
One branch of economics that has grown in importance in the last twenty years is “Game Theory”. For anyone that has seen the movie “A Beautiful Mind” you will know what I am talking about but for everyone else it’s the idea that we all make choices by trying to figure out what other people might also do. Sounds complicated? Don’t worry it will become obvious with the following example.    
So lets’ think about my fantasy of being a runaway slave. Using simple game theory what would actually be the best strategy for a runaway slave to successfully escape his or her servitude?
OK let’s play a simple chase game:
First of all is it better for the rebel slave to run as fast as possible at the start or to run quite slowly?
Assuming a runaway slave has an hour before someone realises he has escaped he has an hour’s head start. If he runs as fast as possible he will quickly tire and will begin to slow down after just a short distance. If on the other-hand he starts at a moderate speed he will be able to keep up this pace for far longer and get far further from the slave owner and plantation. 
His best strategy will depend on what he thinks the slave-master will do – will the slave master go off in pursuit as fast as possible or will the slave master give chase slow and steady? Anyone who has run a 10k race or longer will be able to testify that getting the right pace is everything. Go off too fast and you hit the wall and the slower runners quickly catch up with you and overtake you leaving you gasping. And so the runaway should only run off as quickly as possible if he thinks the slave owner will give pursuit as quickly as possible also, with both of them tiring quite quickly and the slave being able to escape. Otherwise the slow and steady pursuer would always catch the sprinter down the road.
Alternatively if the runaway heads off at a steady pace he is betting that his pursuer will do the same. If the pursuer heads off at a sprint he will be able to catch the runaway before he has got far enough away from the plantation.
So those are the two alternatives for the potential runaway: Fast and furious vs. slow and steady. So what does game theory tell us he should do? 
I believe the best strategy for the slave is to run-away as quickly as possible because in all likelihood the slave owner will want to catch the slave as quickly as possible and will also give chase as quickly as possible. In these circumstances the runaway slave will get away and freedom will be his! 
However what I have just described is called a “static game” – a one off event. In reality this game will be “dynamic” meaning it will be played out several times over many years. (In the US it is estimated that approximately 1,000 slaves tried to escape per year in the first half of the 19th Century). 
In a “dynamic game” the slave master will realise that heading off quickly means the runaway gets away. So after the 4th or 5th slave has successfully got away he will change his strategy and pursue in a slow and steady manner eventually catching up with the tired sprinting slave.
As time progresses the remaining slaves (potential runaways) will realise that sprinting is no longer yielding results and so they too will head off slow and steady. The first lot will get away until the slave owner realises what is happening. At that point the slave owner will start sprinting at the start when giving chase. In this case the slave owner will then catch the runaways who have not got far enough away.
And so in my simple game theory model of runaway slaves the number of successful and unsuccessful escape attempts will go in waves as the different runaways fluctuate between the two strategies and there is a time lag between the slave masters catching up (literally and metaphorically) to the new approach.
I decided to check my game theory approach with my wife who is a professional economist as opposed to myself who hasn’t touched an economics book since graduating twenty years ago. She listened to my dynamic game theory argument and after much thought finally offered her judgement:
“You’ve been blinded by your love of running. The slaves shouldn’t runaway at all – I think game theory would dictate that they stay where they are and fight instead”. Spoken like a true revolutionary.

The recent World Championship Men’s Marathon was a brilliant piece of game theory in action. With two kilometres to go the Ugandan runner Stephen Kiprotich was in the lead but Lelisa Desisa of Ethiopia was right behind him. Now it is easier for the person on the leader’s shoulder to bide his time and then overtake in the last few hundred meters and sprint to victory, so what was Kiprotich to do?
Kiprotich did what any economist would have told him to do, he started to zig-zag. Following someone’s zig-zagging is incredibly tiring (a lot more tiring for the follower than the leader due to the unexpected changes in direction). So if Desisa had followed a straight line and ignored the zig-zagging he would quickly go into the lead then the Ugandan would be on his shoulder and ready to overtake in the last few hundred meters. Follow the zig-zag and Desisa tires himself out. 
It was a masterful piece of game theory by Kiprotich. Whatever option Desisa choice would play to the Ugandan’s advantage. In the end Desisa followed the zig-zagging, became completely tired out and the gold went to the economically minded Stephen Kiprotich.