LEDA: a platform for combinatorial and geometric computing
LEDA: a platform for combinatorial and geometric computing
The Structure and Complexity of Nash Equilibria for a Selfish Routing Game
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
The complexity of pure Nash equilibria
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Nash equilibria in all-optical networks
WINE'05 Proceedings of the First international conference on Internet and Network Economics
On the existence of nash equilibria in strategic search games
TGC'11 Proceedings of the 6th international conference on Trustworthy Global Computing
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In large-scale or evolving networks, such as the Internet, there is no authority possible to enforce a centralized traffic management. In such situations, Game Theory and the concepts of Nash equilibria and Congestion Games [8] are a suitable framework for analyzing the equilibrium effects of selfish routes selection to network delays. We focus here on layered networks where selfish users select paths to route their loads (represented by arbitrary integer weights). We assume that individual link delays are equal to the total load of the link. We focus on the algorithm suggested in [2], i.e. a potential-based method for finding pure Nash equilibria (PNE) in such networks. A superficial analysis of this algorithm gives an upper bound on its time which is polynomial in n (the number of users) and the sum of their weights. This bound can be exponential in n when some weights are superpolynomial. We provide strong experimental evidence that this algorithm actually converges to a PNE in strong polynomial time in n (independent of the weights values). In addition we propose an initial allocation of users to paths that dramatically accelerates this algorithm, compared to an arbitrary initial allocation. A by-product of our research is the discovery of a weighted potential function when link delays are exponential to their loads. This asserts the existence of PNE for these delay functions and extends the result of [2].