Real Mathematics – Social Situations #2

There is only one rule: No rules!

Istanbul is a great city. But some days I feel overwhelmed with its traffic jam. I am aware of the fact that almost every metropolis on earth has the same problems. But there is something you don’t know if you have never driven a car in Istanbul: Everything could happen in Istanbul’s traffic.

In this city if there is a pedestrian and a car on a pedestrian crossing it is the pedestrian who gives way, not the car. In this city it is absolutely normal to see a car on the far right lane trying to make a left turn. In this city if multiple cars meet at a crossing, nobody knows who will be the first car to pass.

This poor reporter is trying to use the pedestrian lane. You can see what kind of situation she got into. Don’t worry; she is fine. She’s made it safe and sound.

These are just a few examples of how irregular traffic is in Istanbul. You might think that I am exaggerating. Okay, you can continue to think like that, just beware even if it is green light for you.

What strikes me most about Istanbul’s traffic is that everybody learns about these rules when they study for the driving license exam. However most of the drivers forget about who has priority at a crossroads.

Who will lose?

Assume that you are the driver 1 and you are coming closer to an intersection where you have the priority to pass. Unfortunately for you, this intersection is in Istanbul and you have no idea how the driver 2 will behave in the next few seconds: Will he/she stop or not?

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Situation 1: You both decided to stop. Both cars are stopping in the middle of the road and no one is crossing the intersection. There are no winners.

Situation 2: You both decided not to stop and eventually crashed. In this situation not only there are no winners, you two are both losers.

Situation 3: You decided to stop, and driver 2 didn’t. Driver 2 won the game as he/she is the first one the pass the intersection.

Situation 4: You decided not to stop as driver 2 did. You are the crowned winners: You will be home 3 seconds before driver 2.

Nash Equilibrium

Let’s use game theory to analyze these four situations. If a car stops it will get 0, if they crashed they’ll each get -1 and if one passes first he/she will get 1 point.

Then, matrix of the game will be as follows:

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If drivers are selfish, meaning that everyone is looking out for their own interest, both drivers would decide to get 1 point. This means they would both decide not to stop and crash.

Yet, Nash equilibrium of this game demonstrates interesting results.

If either one of them stops as the other one knows about it, then the other driver would choose not to stop.

If either one of them doesn’t stop as the other one knows about it, then the other driver would choose to stop. This way he/she can prevent the crash.

This means that the situation has two Nash equilibriums: (1,0) or (0,1).

In these types of games every player needs one another. As seen above in certain situations drivers must think of preventing an accident instead of passing the intersection first.

A person needing one another is a necessity if we all want a just and organized social life. If every individual in a society keeps thinking only about his/her own interests and makes decisions which would only help themselves, then every aspect of social life would get worse than it should be. This is the case why traffic of Istanbul is in such conditions: Drivers don’t respect others and disobey social contracts just because they have something personal to gain.

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“Thou shalt not steal!” Oh you are driving… Sure, you can steal my time!

An example from Istanbul: A driver has to wait in traffic for 50 minutes even though that distance can be taken in 10 minutes with normal speed limit. After having spent 50 frustrating minutes, this driver would double or even triple a single lane so that he/she would gain 5 minutes. Driver’s decision to double a single lane makes traffic even denser; it would affect thousands of people. And craziest of all is that this driver’s behavior is not any different from the ones who initiated the traffic jam in the first place…

M. Serkan Kalaycıoğlu

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