List of PPAD-complete problems

This is a list of PPAD-complete problems.

Fixed Point Theorems[]

• Sperner's lemma
• Brouwer fixed point theorem
• Kakutani fixed point theorem

Game theory[]

• Nash equilibrium
• Core of Balanced Games

Equilibria in Game Theory and Economics[]

• Fisher market equilibria
• Arrow-Debreu Equilibria
• Approximate Competitive Equilibrium from Equal Incomes
• Finding clearing payments in financial networks

Graph theory[]

• (see also the NP-complete Hypergraph matching)

Miscellaneous[]

• Scarf's Lemma

References[]

• Papadimitriou, Christos (1994). "On the Complexity of the Parity Argument and Other Inefficient Proofs of Existence". Journal of Computer and System Sciences. 48 (3): 498–532. doi:10.1016/S0022-0000(05)80063-7. Paper available online at Papadimitriou's Homepage.
• C. Daskalakis, P.W. Goldberg and C.H. Papadimitriou (2009). "The Complexity of Computing a Nash Equilibrium". SIAM Journal on Computing. 39 (3): 195–259. CiteSeerX 10.1.1.68.6111. doi:10.1137/070699652.
• Xi Chen and Xiaotie Deng (2006). "Settling the complexity of two-player Nash equilibrium". In Proc. 47th FOCS. pp. 261–272.