Tuesday, 22 March 2011

Game Theory and Junction Blocking

Game theory divides games into those in which all information is visible to all players (like chess), and those where each side holds secrets (like poker). There are different tactics in each. In a game when the position and intent of all players is visible the Nash Equilibrium -the steady state reached when every player can predict the optimal moves of their opponents and act accordingly- is easier to reach.

In junctions, it comes down to "do you block the junction or not". Here on Cheltenham Road the taxi says yes.
Then, just before the lights change, it moves forward and another car makes the same decision.

Here in this video from the St Michaels Hill roundabout, you can see another taxi making the same decision.

In highway-code theory, blocking junctions is selfish and can lead to total gridlock.

In Game Theory, as applied to Bristol City streets, blocking the junction is the correct thing to do. why?
  1. You know that nobody is going to penalise anyone who blocks a junction.
  2. If you block a junction, when the road ahead eventually moves, you will get through.
  3. If the other players in the game -the other vehicles who get time at the lights, block the junction, you don't get a chance to drive yourself, hence will never make progress.
  4. You are therefore forced to pull out and block the lane -if you know the other players will do the same thing.
  5. The other players know the same thing, -that your best strategy to make progress is to pull out and block the lane.
  6. Therefore they will pull out and block the lane themselves, as it is the only way they make progress.
  7. Therefore your best strategy, given your knowledge of their best strategy, is to pull out.
This is the Nash Equilibrium: the steady state where no player in the game has any incentive to change their strategy. If any driver at the front of the lights doesn't pull out and block the junction, all they will do is annoy the cars behind.

This is why drivers in the city don't get annoyed by other cars doing this. They'd do the same thing. The only way to change this would be to change assumption (1), that there is no penalty for blocking a junction.

Game Theory: the maths you can play on the commute. Even if you don't realise it.

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