6.896 Topics in Algorithmic Game Theory March 1, 2010 Lecture 8
نویسندگان
چکیده
The complexity class PPAD (“Polynomial Parity Argument on Directed Graphs”) was proposed by Christos Papadimitriou in 1994 [6]. Its goal is to capture the complexity of searching for an object whose existence is guaranteed by the principle that, “A directed graph with an unbalanced node (indegree 6= outdegree) must have another unbalanced node.” Suppose that we describe an exponentially large graph with vertex set {0, 1}, where each vertex has in-degree and out-degree at most 1 by providing two circuits, P and N . Each circuit takes as input a node id (a string in {0, 1}) and outputs a node id (another string in {0, 1}). We interpret our graph as having a directed edge from v1 to v2 iff the following two properties hold:
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