During the last two lectures we've focused on "routing games" a.k.a. "congestion games" where sources must choose the route they (or their packets) take through a network to a destination. We've gone through the same set of analyses we did for load balancing games -- We studied the existence and the efficiency of Nash equilibria. We saw that Nash equilibria need not exist, but that in the case of linear latency functions they will always exist and, not only that, they will be quite efficient (i.e. small "price of anarchy"). But, unlike load balancing games, the "price of stability" is not 1, and so the optimal routes are no longer always an equilibrium.
In addition to the particular application of routing games, we also introduced the class of "potential games" which has a number of important properties that helped us in our analysis. Further, we saw an example of the technique of "marginal cost pricing", which can be used to align the local incentives of players with the global goal. These two concepts are important and useful far beyond routing games.
Next class, we'll leave routing games and move on to the study of Ad auctions.
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