What is "ppad"

In computer science, PPAD ("Polynomial Parity Arguments on Directed graphs") is a complexity class introduced by Christos Papadimitriou in 1994. PPAD is a subclass of TFNP based on functions that can be shown to be total by a parity argument. The class attracted significant attention in the field of algorithmic game theory because it contains the problem of computing a Nash equilibrium, and this problem was shown by Chen and Deng in 2005 to be complete for the class.

PPAD is a class of problems that are believed to be hard, but obtaining PPAD-completeness is a weaker evidence of intractability than that of obtaining NP-completeness. PPAD problems cannot be NP-complete, for the technical reason that NP is a class of decision problems, but the answer of PPAD problems is always yes, as a solution is known to exist, even though it might be hard to find that solution. It could still be the case that PPAD is the same class as P, and still have that P  ≠  NP, though it seems unlikely. Examples of PPAD-complete problems include finding Nash equilibria, computing fixed points in Brouwer functions, finding Arrow-Debreu equilibria in markets and more.