Bottleneck Games in Noncooperative Networks

We consider routing games where the performance of each user is dictated by the worst (bottleneck) element it employs. We are given a network, finitely many (selfish) users, each associated with a positive flow demand, and a load-dependent performance function for each network element. We first prove the existence of a Nash equilibrium, considering two routing scenarios, namely when a user can split its traffic over more than one path (splittable bottleneck game) and when it cannot (unsplittable bottleneck game); we also consider the convergence properties of each game. Then, we turn to investigate the efficiency of the Nash equilibria in both games with respect to the network optimum in terms of bottleneck performance; specifically, while for both games we show that the price of anarchy is unbounded, we identify for each game conditions under which Nash equilibria are optimal. Finally, we analyze for each game the performance deterioration at Nash equilibria with respect to the additive network performance objective of "total cost". Keywordsbottleneck & additive metrics, Nash equilibrium, price of anarchy, price of stability, selfish routing, unregulated traffic.