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The Driving Theory

Problem:

Each year, there are over 530,000 auto accidents in Tunisia. According to the latest WHO data published in May 2014 Road Traffic Accidents Deaths in Tunisia reached 2,007 or 3.75% of total deaths.  From all these accidents, 4.73% are caused by hazardous weather and poor visibility (Tunisian Ministry of Transport)

In Tunisia, driving at night often means extremely poor visibility – particularly in areas where there is insufficient street lighting. When there is poor visibility, every driver uses the different types of lights in his car in order to improve his own visibility. The two different lights available for use are high beam and low beam which offers two different ranges of sight.

While High Beam lights offer a very long range, they tremendously negatively affect the visibility of drivers driving in the opposite direction.  Especially in a two-way street, the lights of the upcoming cars in the opposite directions can be blinding.

The Mathematical Model:

Every time we want to model a situation using game theory, it is crucial to identify these key components:

Players:

A strategic decision maker within the context of the game. In this situation, the two drivers driving in opposite directions are the two players.

Strategies:

A complete plan of action a player will take given the set of circumstances that might arise within the game. In this situation, the two possible strategies are Use of High Beam/ Use of Low Beam.

Payoffs:

The payout a player receives from arriving at a particular outcome. The payout can be in any quantifiable form, from dollars to utility. In this situation, the payout is the quality of visibility.

-Using High Beam gives +3 for the user and -2 for the opposite driver.

-Using Low Beam gives +2 for the user and does not affect the opposite driver.

To simplify and compile all these data, we build this table called a “Matrix”.

We will approach this situation from Driver 2 perspective. If Driver 1 is going to use the High Beam, it is better for Driver 2 to use the High Beam because it has a higher a payout.

If Driver 1 is going to use Low Beam, it is better for Driver 2 to use High Beam because it has a higher payoff two.

Thus for Driver 2, it is always better to use the High Beam as it is guaranteed it will give him a higher payoff regardless of which strategy Driver 1 takes. In this case, we say the strategy High Beam dominates the strategy Low Beam.

If we use the same reasoning for Driver 1, we will reach the same conclusion. It is always better for him to use the High Beam regardless of what Driver 2 does.

Conclusion:

As a conclusion, High Beam/ High Beam is a solution for this game. However, we can clearly see that Low Beam/Low Beam offers a better payout for both players (2,2) instead of (1,1).  This situation is know in game theory as the prisoner’s dilemma. The prisoner’s dilemma is a standard example of a game analyzed in that shows why two completely “rational” individuals might not cooperate, even if it appears that it is in their best interests to do so. So in this driving situation, it is crucial for the two drivers to cooperate and use Low Beam instead of High Beam as it is better for both players even though from a rational and non-cooperative point of view it is better to use High Beam.

 

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