computer science, PPAD ("Polynomial Parity Arguments on Directed graphs") is a complexity class introduced by Christos Papadimitriou in 1994. PPAD is a subclass...

Goldwasser. The complexity of decision versus search. SIAM Journal on Computing, Vol. 23, No. 1, February 1994. Daskalakis, Costis (2015). "22. PPAD". MIT OpenCourseWare...

that introduced PPAD and PPA. PPP contains both PPAD and PWPP (polynomial weak pigeonhole principle) as subclasses. These complexity classes are of particular...

is reducible to that problem. PPAD is defined in a similar way to PPA, except that it is defined on directed graphs. PPAD is a subclass of PPA. This is...

This is a list of PPAD-complete problems. Sperner's lemma Brouwer fixed-point theorem Kakutani fixed-point theorem Nash equilibrium Core of Balanced Games...

Combinatorial game theory measures game complexity in several ways: State-space complexity (the number of legal game positions from the initial position)...

Hollender, Alexandros; Savani, Rahul (11 November 2020). "The Complexity of Gradient Descent: CLS = PPAD ∩ PLS". arXiv:2011.01929 [cs.CC]. Thieme, Nick (2021-08-17)...

equilibria for one-shot finite games, a problem which lies in the PPAD complexity class. The practical consequence of this is that no efficient (polynomial-time)...

Additionally, if iO and one-way functions exist, then problems in the PPAD complexity class are provably hard. However, indistinguishability obfuscation...

of complexity classes in computational complexity theory. For other computational and complexity subjects, see list of computability and complexity topics...

in such a sparse game is PPAD-hard, and that there does not exist a fully polynomial-time approximation scheme unless PPAD is in P. In symmetric games...

algorithms for finding equilibria. Of special importance is the complexity class PPAD, which includes many problems in algorithmic game theory. Mechanism...

that a complexity class called CLS (Continuous Local Search) is equal to the intersection of PPAD and PLS. Equilibria, fixed points, and complexity classes:...

polynomial (the problem is PPAD-hard even with goods), it runs fast on random instances. It also proves that the problem is in PPAD, the solutions are rational-valued...

Sperner's lemma), and therefore it is PPAD-complete. This implies that computing an approximate fixed-point is PPAD-complete even for very simple functions...

utilities, computing a CE is PPAD-hard. Their proof shows also that this market-equilibrium problem does not have an FPTAS unless PPAD is contained in P. When...

problem does not have a fully polynomial-time approximation scheme, unless PPAD ⊆ P. On the other hand, there are algorithms for finding an approximate equilibrium...

was first studied by Christos Papadimitriou. He introduced a complexity class called PPAD, which contains this as well as related problems (such as finding...

He defined the complexity class PPA to encapsulate problems such as this one; a closely related class defined on directed graphs, PPAD, has attracted...

positions (the state space complexity) or the 26,830 possible games up to rotations and reflections (the game tree complexity) on this space. If played...

chess, backgammon, tic-tac-toe, and Go, with decision trees varying in complexity—from the compact tree of tic-tac-toe to the vast, unmappable tree of chess...

hard or even complete for some complexity class C {\displaystyle C} , in particular NP-hard (but often also PSPACE-hard, PPAD-hard, etc.). This means that...

unless PPAD is in P. Chen and Teng proved PPAD-hardness in a Fisher market with SPLC utilities. Chaudhury, Garg, McGlaughlin and Mehta proved PPAD-hardness...

Chess Fully solving chess remains elusive, and it is speculated that the complexity of the game may preclude it ever being solved. Through retrograde computer...

Other Topics Bertrand paradox Chainstore paradox Computational complexity of games Helly metric Multi-agent system PPAD-complete...

solved at least weakly. Calculated estimates of game-tree complexity and state-space complexity of chess exist which provide a bird's eye view of the computational...

(does not depend on n). Then, finding an ε-approximate consensus-halving is PPAD-hard, which is theoretically weaker than PPA-hard. The proof is by reduction...

Other Topics Bertrand paradox Chainstore paradox Computational complexity of games Helly metric Multi-agent system PPAD-complete...

way may not necessarily be NP-complete, as it is unknown whether PPA = NP. PPAD is an analogous class defined on implicit directed graphs that has attracted...

Other Topics Bertrand paradox Chainstore paradox Computational complexity of games Helly metric Multi-agent system PPAD-complete...