Traffic congestion, pollution and the prisoners' dilemma

Earlier this week, Matt Heath wrote an interesting column in the New Zealand Herald, talking about his transport preferences:

I've been flirting with different ways of getting around Auckland and nothing beats the door-to-door comfort, convenience and in-house entertainment of your own vehicle.

Heath does a good job of identifying the main culprit when it comes to traffic congestion and pollution:

Whatever anyone says, driving to work is easier and way more fun [than taking the bus].

As for the pollution there's a simple equation. If most people stopped driving there could be a significant difference. But if only I stop driving it won't make any difference. I can't save the world on my own. If everyone stops, it's logical for me to continue driving because the roads would be clear and the air fresh anyway. If everyone is driving, I'd drive too because one person isn't going to be the difference that saves the world. Selfish but logical.

He's describing an example of the prisoners' dilemma, which I've also described earlier here. Consider the decisions of two commuters only (A and B), who can decide to drive, or take the bus. For simplicity, let's also assume this is a non-repeated game (which it clearly isn't of course). If both commuters choose to drive, then both face traffic congestion and pollution. If one drives and the other takes the bus, then the driver has a free and clear commute to work, while the other has the loss of fun associated with bus travel (as explained by Matt Heath). If both take the bus, then both face the loss of fun. One last assumption - the loss of fun from taking the bus is worse than suffering the congestion and pollution associated with everyone driving (which is why Matt Heath decided to drive rather than take the bus). The game in normal (payoff table) form is as follows:

What happens in this game? Consider Commuter A first. They have a dominant strategy to drive. This is because the payoff is always better than taking the bus. If Commuter B drives, Commuter A is better off driving (because suffering the congestion and pollution is better than the loss of fun associated with taking the bus, at least according to Matt Heath!). If Commuter B takes the bus, Commuter A is better off driving (because having a free and clear trip to work is better than the loss of fun associated with taking the bus). So Commuter A should choose to drive, because driving always results in a higher payoff.

Now consider Commuter B. They also have a dominant strategy to drive, because the payoff is always better than taking the bus. If Commuter A drives, Commuter B is better off driving (because suffering the congestion and pollution is better than the loss of fun associated with taking the bus). If Commuter A takes the bus, Commuter B is better off driving (because having a free and clear trip to work is better than the loss of fun associated with taking the bus). So Commuter B should choose to drive, because driving always results in a higher payoff.

So, there is a unique Nash equilibrium (and dominant strategy equilibrium) in this game, where both commuters choose to drive to work. Even though pollution and congestion would be less if both took the bus. Unfortunately, this result will hold even if we extend the game to many players, or if we treat it as a repeated game. Which is why we suffer our way through traffic jams every day on the way to work.