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Assignment: Braess's paradox
Consider the nonatomic routing game shown in the left figure (i) below. One unit of splittable traffic must travel from A to D. The delay functions are marked alongside the respective edges, for example, the time to traverse edge AB is 2 + u if a fraction u of traffic uses that edge.
Figure 1: Braess's Paradox.
(a) What is the "equilibrium" of the game in (i), and the corresponding travel time of all traffic?
[Hint: In equilibrium x = v and y = u. You may use this fact without justification. You should solve three equations in x, y, and w alone. Two of these equations will be "flow equations", the last will be an indifference equation.]
The assignment consists of writing an extended abstract of the article - A coinductive calculus of binary trees
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