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We prove that Bimatrix, the problem of finding a Nash equilibrium in a two-player game, is complete for the complexity class <b>PPAD</b> (Polynomial Parity Argument, Directed version) introduced by Papadimitriou in 1991. Our result, building upon the work of Daskalakis et al. [2006a] on the complexity of four-player Nash equilibria, settles a long standing(More)
Even though many people thought the problem of finding Nash equilibria is hard in general, and it has been proven so for games among three or more players recently, it's not clear whether the two-player case can be shown in the same class of PPAD-complete problems. We prove that the problem of finding a Nash equilibrium in a two-player game is PPAD-complete
We are interested in the problem of word extraction from Chinese text collections. We define a word to be a meaningful string composed of several Chinese characters. For example, , ‘percent’, and , ‘more and more’, are not recognized as traditional Chinese words from the viewpoint of some people. However, in our work, they are words because they are very(More)
We wish to explore all edges of an unknown directed, strongly connected graph. At each point, we have a map of all nodes and edges we have visited, we can recognize these nodes and edges if we see them again, and we know how many unexplored edges emanate from each node we have visited, but we cannot tell where each leads until we traverse it. We wish to(More)