Routing Games: Pigou's example

In class today we looked at the Routing Games. We did this by considering Pigou’s Example.

You can see a recording of this here.

Pigou’s example is a simple model of congestion there are 2 choices available to traffic, the first is not affected by traffic, the other is heavily affected by traffic (the more people using it, the worse it is).

This simple situation is modelling as a routing game which requires the network diagram and congestion functions you can see here:

The calculations we carried out included:

• Identifying the most efficient flow: half the population take each edge.
• Identifying the Nash flow: the entire population using the shortcut (making it as slow as the other way)
• Finding the Nash flow by optimising the Potential function.
• Finding the optimal flow by finding the Nash flow for a slightly modified game.

The final thing I spoke about was Braess’ Paradox which is an important idea, it is theoretically interesting but empirically has real negative implications: adding capacity to networks may lead to a worse performance.