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In a system where noncooperative agents share a common resource, we propose the price of anarchy, which is the ratio between the worst possible Nash equilibrium and the social optimum, as a measure of the effectiveness of the system. Deriving upper and lower bounds for this ratio in a model where several agents share a very simple network leads to some(More)
We define a natural variant of NP, MAX NP, and also a subclass called MAX SNP. These are classes of optimization problems, and in fact contain several natural, well-studied ones. We show that problems in these classes can be approximated with some bounded error. Furthermore, we show that a number of common optimization problems are complete for MAXSNP under(More)
In the Multiterminal Cut problem we are given an edge-weighted graph and a subset of the vertices called terminals, and asked for a minimum weight set of edges that separates each terminal from all the others. When the number k of terminals is two, this is simply the min-cut, max-flow problem, and can be solved in polynomial time. We show that the problem(More)
We define several new complexity classes of search problems, "between" the classes FP and FNP. These new classes are contained, along with factoring, and the class PLS, in the class TFNP of search problems in FNP that always have a witness. A problem in each of these new classes is defined in terms of an implicitly given, exponentially large graph. The(More)
We resolve the question of the complexity of Nash equilibrium by showing that the problem of computing a Nash equilibrium in a game with 4 or more players is complete for the complexity class PPAD. Our proof uses ideas from the recently-established equivalence between polynomial time solvability of normal form games and graphical games, establishing that(More)
We present an algorithm for determining the shortest path between a source and a destination on an arbitrary (possibly nonconvex) polyhedral surface. The path is constrained to lie on the surface, and distances are measured according to the Euclidean metric. Our algorithm runs in time O(n log n) and requires O(n2) space, where n is the number of edges of(More)
We introduce a novel game that models the creation of Internet-like networks by selfish node-agents without central design or coordination. Nodes pay for the links that they establish, and benefit from short paths to all destinations. We study the Nash equilibria of this game, and prove results suggesting that the "price of anarchy" [4] in this context (the(More)