The Emergence of Conventions- The Crossroads Game

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Game theory can explain the emergence of road rules, as the outcome of two drivers passing each other depends on their spontaneous actions and not on a pre-designed system of rules.


Consider the following example. Suppose that you, Driver 1 (D 1) are approaching an intersection. Another car driving in the opposite direction by Driver 2 (D 2) gets at the intersection at the same time.


Since you both have to cross the intersection, you as D1 have two options: you can either slow down and let the other car pass or you can maintain speed.

Suppose D 1 has an expectation of ? that D 2 will slow down and an expectation of 1 - ? that D 2 will maintain speed, where ? ? (0.1)

Suppose D 2 has an expectation of ? that D 1 will slow down and an expectation of 1 - ? that D 1 will maintain speed, where ? ? (0.1).

Below are the payoffs measured in the time drivers lose at the intersection. If one of the drivers slows down and the other one maintains speed, the one who slowed down will lose one minute. If both drivers slow down, they will each lose 10 minutes, as they have to decide who will gain priority in crossing the road (although 10 minutes is clearly exaggerated, assume that number of minutes for the purpose of this game). If both drivers maintain speed, they will collide, which will result in each one losing 21 minutes (assess and agree on the damages, exchange insurance information, etc.), in addition to later on having to incur some cost for repairing their cars.


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