Traffic Jam – a game theoretic model of an everyday problem

This is how a typical traffic jam builds up. Consider peak hour, or a rainy evening. Traffic from an arterial road enters a narrow road. As the throughput slows, a queue forms and grows at a traffic light, or a temporary obstruction. Traffic jams occur because motorists play their dominant strategies – jump the queue. Their choice can, however, be influenced by one of two ways.

John joining at the end of the queue does not know how long the stack is. He has two choices. He can join the queue, or jump it by driving on the right (wrong, really!) side of the road to get nearer the head. If he joins the queue (and others do, too), the traffic will clear in an orderly fashion after a wait of say, 10 minutes. If he jumps the queue, and others don’t, he will get away in say, 5 minutes.

The problem is others think the same way. Motorists crowding the right lane from both ends of the road will cause a terrible obstruction. Everyone will get stuck, but those who jumped the queue will usually get away quicker than those who stayed back. However, it is clear that they will take longer than if everyone had stayed in their lanes. Let us say the drivers who jumped the queue now take 20 minutes to clear the traffic.

The bottleneck will, however, create problems for Bob who was right behind John but decided to join the queue as a good citizen. He will take even longer, 30 minutes, to clear the traffic and be on his way home. Remember he had a choice: he could have jumped the queue like John did. The following table represents this scenario.

Payoff in minutes
Traffic Jam - a game theoretic model of an everyday problem

  • We can see that if Bob joins the queue, John can improve his getaway time from 10 to 5 minutes by jumping it. The same is true of Bob. Thus, jumping the queue is the dominant strategy for both. They do precisely that and cause the traffic jams we often experience on our roads. In the process, Bob and John suffer even as they bring suffering to others.
  • Traffic jams occur because motorists play their dominant strategies – jump the queue. Their choice can, however, be influenced by one of two ways.
  • The payoff for jumping the queue can become negative if this behaviour is    detected and punished. Vigilant and strict policing can alter the apparent    benefit of disorderly behaviour. The time that was saved on the road may now    be spent standing in the queue to pay the fine. Or, the penalty may be steep    enough to encourage staying in the correct lane. This, though, is a short-term    solution. Take away policing and the traffic may return to its disorderly    conduct.
  • If the difference between payoffs for jumping the queue and obeying rules    were to be small, it is likely that most people will stay in their lanes. The rule    breaker now saves five minutes by driving on the wrong side of the road if    others stay in their lanes. If he saved only a minute or two he might persuade himself to be a law-abiding motorist. Wider roads are thus a more permanent    solution.
  • The combination of the above two methods is likely to be an even more    potent solution. Low traffic density reduces the gain from breaking traffic    rules. Getting caught and being slapped with a fine increases the cost of violation.

Perhaps this explains why in India we drive with complete disregard for traffic rules, but play law-abiding motorists in Singapore and London.