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Complexity class
computer science, PPAD ("Polynomial Parity Arguments on Directed graphs") is a complexity class introduced by Christos Papadimitriou in 1994. PPAD is a subclass
PPAD_(complexity)
Complexity class
that introduced PPAD and PPA. PPP contains both PPAD and PWPP (polynomial weak pigeonhole principle) as subclasses. These complexity classes are of particular
PPP_(complexity)
Complexity class
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
PPA_(complexity)
Complexity class
Goldwasser. The complexity of decision versus search. SIAM Journal on Computing, Vol. 23, No. 1, February 1994. Daskalakis, Costis (2015). "22. PPAD". MIT OpenCourseWare
FNP_(complexity)
Notion in combinatorial game theory
Combinatorial game theory measures game complexity in several ways: State-space complexity (the number of legal game positions from the initial position)
Game_complexity
Type of cryptographic software obfuscation
Additionally, if iO and one-way functions exist, then problems in the PPAD complexity class are provably hard. However, indistinguishability obfuscation
Indistinguishability obfuscation
Indistinguishability_obfuscation
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
List of PPAD-complete problems
List_of_PPAD-complete_problems
Hollender, Alexandros; Savani, Rahul (2022-12-19). "The Complexity of Gradient Descent: CLS = PPAD ∩ PLS". Journal of the ACM. 70 (1): 7:1–7:74. arXiv:2011
FIXP
Complexity class
W.; Hollender, Alexandros; Savani, Rahul (2023). "The Complexity of Gradient Descent: CLS = PPAD ∩ PLS". Journal of the ACM. 70: 1–74. arXiv:2011.01929
TFNP
Study of algorithms in strategic environments
for computing Nash equilibria. The problem is complete for the complexity class PPAD even in 2-player games. In contrast, correlated equilibria can be
Algorithmic_game_theory
Class of theorems about Nash equilibrium payoff profiles in repeated games
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)
Folk_theorem_(game_theory)
Algorithm analysis method
smoothed complexity polynomial in n and 1/s, where s is the input perturbation size, unless PPAD ≤ RP. In particular, the smoothed complexity of the Lemke-Howson
Smoothed_analysis
Complexity class
that a complexity class called CLS (Continuous Local Search) is equal to the intersection of PPAD and PLS. Equilibria, fixed points, and complexity classes:
PLS_(complexity)
of complexity classes in computational complexity theory. For other computational and complexity subjects, see list of computability and complexity topics
List_of_complexity_classes
Economical computational problem
smoothed complexity polynomial in n and 1/s, where s is the input perturbation size, unless PPAD ≤ RP. In particular, the smoothed complexity of the Lemke-Howson
Nash_equilibrium_computation
Game in algorithmic game theory
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
Succinct_game
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
Arrow–Debreu_exchange_market
Computing the fixed point of a function
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
Fixed-point_computation
Economical computational problem
unless PPAD is in P. Chen and Teng proved PPAD-hardness for a Fisher market with SPLC utilities. Chaudhury, Garg, McGlaughlin and Mehta proved PPAD-hardness
Market equilibrium computation
Market_equilibrium_computation
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
Fisher_market
Logical paradox in decision-making theory
Bertrand paradox Chainstore paradox Computational complexity of games Helly metric Multi-agent system PPAD-complete Mathematics portal Game theory WikiProject
Paradox_of_tolerance
Algorithm in game theory
Bertrand paradox Chainstore paradox Computational complexity of games Helly metric Multi-agent system PPAD-complete Mathematics portal Game theory WikiProject
Paranoid_algorithm
Solution concept in Game Theory
Bertrand paradox Chainstore paradox Computational complexity of games Helly metric Multi-agent system PPAD-complete Mathematics portal Game theory WikiProject
Bayes_correlated_equilibrium
Every graph has evenly many odd vertices
He defined the complexity class PPA to encapsulate problems such as this one; a closely related class defined on directed graphs, PPAD, has attracted
Handshaking_lemma
Political model of international conflict resolution
Bertrand paradox Chainstore paradox Computational complexity of games Helly metric Multi-agent system PPAD-complete Mathematics portal Game theory WikiProject
Two-level_game_theory
Type of fair division
(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
Consensus_splitting
Solution concept in Game Theory
Bertrand paradox Chainstore paradox Computational complexity of games Helly metric Multi-agent system PPAD-complete Mathematics portal Game theory WikiProject
Cursed_equilibrium
Paper-and-pencil game for two players
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
Tic-tac-toe
Italian economist (born 1961)
Bertrand paradox Chainstore paradox Computational complexity of games Helly metric Multi-agent system PPAD-complete Mathematics portal Game theory WikiProject
Pierpaolo_Battigalli
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
Leontief_utilities
Concept in game theory
Bertrand paradox Chainstore paradox Computational complexity of games Helly metric Multi-agent system PPAD-complete Mathematics portal Game theory WikiProject
Focal_point_(game_theory)
Finding an optimal algorithm for playing chess
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
Solving_chess
Bertrand paradox Chainstore paradox Computational complexity of games Helly metric Multi-agent system PPAD-complete Mathematics portal Game theory WikiProject
Contingent_cooperator
Hypothesis in computational complexity theory
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
Computational hardness assumption
Computational_hardness_assumption
Branch of game theory about two-player sequential games with perfect information
greater weight on theoretical results, including the analysis of game complexity and the existence of optimal strategies through methods like the strategy-stealing
Combinatorial_game_theory
Decision rule used for minimizing the possible loss for a worst-case scenario
Bertrand paradox Chainstore paradox Computational complexity of games Helly metric Multi-agent system PPAD-complete Mathematics portal Game theory WikiProject
Minimax
Class of games where players choose their actions sequentially
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
Sequential_game
Game whose outcome can be correctly predicted
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
Solved_game
Game theory case weighing own/others' sacrifice
Bertrand paradox Chainstore paradox Computational complexity of games Helly metric Multi-agent system PPAD-complete Mathematics portal Game theory WikiProject
Volunteer's_dilemma
Transactional view of violent conflict in international relations theory
Bertrand paradox Chainstore paradox Computational complexity of games Helly metric Multi-agent system PPAD-complete Mathematics portal Game theory WikiProject
Bargaining_model_of_war
Situation where total gains match total losses
Bertrand paradox Chainstore paradox Computational complexity of games Helly metric Multi-agent system PPAD-complete Mathematics portal Game theory WikiProject
Zero-sum_game
Type of perfect Bayesian equilibrium
Bertrand paradox Chainstore paradox Computational complexity of games Helly metric Multi-agent system PPAD-complete Mathematics portal Game theory WikiProject
Separating_equilibrium
Theorem on triangulation graph colorings
was first studied by Christos Papadimitriou. He introduced a complexity class called PPAD, which contains this as well as related problems (such as finding
Sperner's_lemma
Concept in game theory
Bertrand paradox Chainstore paradox Computational complexity of games Helly metric Multi-agent system PPAD-complete Mathematics portal Game theory WikiProject
Shapley_value
Theorem in game theory
satisfy certain restrictions on their variation. Scott Aaronson studied the complexity and rate of convergence of various types of dialogues with more than two
Aumann's_agreement_theorem
Economic Model
Bertrand paradox Chainstore paradox Computational complexity of games Helly metric Multi-agent system PPAD-complete Mathematics portal Game theory WikiProject
Bertrand–Edgeworth_model
Preference of known risks to unknown risks
Bertrand paradox Chainstore paradox Computational complexity of games Helly metric Multi-agent system PPAD-complete Mathematics portal Game theory WikiProject
Ambiguity_aversion
Tendency to overestimate in auctions
Bertrand paradox Chainstore paradox Computational complexity of games Helly metric Multi-agent system PPAD-complete Mathematics portal Game theory WikiProject
Winner's_curse
English saying meaning "equivalent retaliation"
Bertrand paradox Chainstore paradox Computational complexity of games Helly metric Multi-agent system PPAD-complete Mathematics portal Game theory WikiProject
Tit_for_tat
Game theory concept
Bertrand paradox Chainstore paradox Computational complexity of games Helly metric Multi-agent system PPAD-complete Mathematics portal Game theory WikiProject
Game_form
Variation of minimax game tree search
Bertrand paradox Chainstore paradox Computational complexity of games Helly metric Multi-agent system PPAD-complete Mathematics portal Game theory WikiProject
Negamax
Search algorithm
; Wigderson, A. (1986). "Probabilistic Boolean Decision Trees and the Complexity of Evaluating Game Trees". 27th Annual Symposium on Foundations of Computer
Alpha–beta_pruning
Concept in conflict studies
Bertrand paradox Chainstore paradox Computational complexity of games Helly metric Multi-agent system PPAD-complete Mathematics portal Game theory WikiProject
Conflict_escalation
Concept in game theory involving long-term strategic planning
Bertrand paradox Chainstore paradox Computational complexity of games Helly metric Multi-agent system PPAD-complete Mathematics portal Game theory WikiProject
Farsightedness_(game_theory)
Decrease in severity of conflicts
Bertrand paradox Chainstore paradox Computational complexity of games Helly metric Multi-agent system PPAD-complete Mathematics portal Game theory WikiProject
De-escalation
Overuse of a shared resource
Bertrand paradox Chainstore paradox Computational complexity of games Helly metric Multi-agent system PPAD-complete Mathematics portal Game theory WikiProject
Tragedy_of_the_commons
Standard example in game theory
tournament. The programs that were entered varied widely in algorithmic complexity, initial hostility, capacity for forgiveness, and so forth. Axelrod discovered
Prisoner's_dilemma
Israeli psychologist (1937–1996)
Bertrand paradox Chainstore paradox Computational complexity of games Helly metric Multi-agent system PPAD-complete Mathematics portal Game theory WikiProject
Amos_Tversky
Solution concept in cooperative game theory
Bertrand paradox Chainstore paradox Computational complexity of games Helly metric Multi-agent system PPAD-complete Mathematics portal Game theory WikiProject
Myerson_value
Model of conflict for two players in game theory
Bertrand paradox Chainstore paradox Computational complexity of games Helly metric Multi-agent system PPAD-complete Mathematics portal Game theory WikiProject
Chicken_(game)
Combinatorial game theory theorem
Bertrand paradox Chainstore paradox Computational complexity of games Helly metric Multi-agent system PPAD-complete Mathematics portal Game theory WikiProject
Sprague–Grundy_theorem
Bertrand paradox Chainstore paradox Computational complexity of games Helly metric Multi-agent system PPAD-complete Mathematics portal Game theory WikiProject
Strategic_move
Problem in game theory
Bertrand paradox Chainstore paradox Computational complexity of games Helly metric Multi-agent system PPAD-complete Mathematics portal Game theory WikiProject
Airport_problem
Situation where all parties are worse off
Bertrand paradox Chainstore paradox Computational complexity of games Helly metric Multi-agent system PPAD-complete Mathematics portal Game theory WikiProject
No-win_situation
Bertrand paradox Chainstore paradox Computational complexity of games Helly metric Multi-agent system PPAD-complete Mathematics portal Game theory WikiProject
Coalition-proof Nash equilibrium
Coalition-proof_Nash_equilibrium
Mathematical modelling of phenotypic evolution
Bertrand paradox Chainstore paradox Computational complexity of games Helly metric Multi-agent system PPAD-complete Mathematics portal Game theory WikiProject
Evolutionary invasion analysis
Evolutionary_invasion_analysis
Search heuristic for combinatorial games
Bertrand paradox Chainstore paradox Computational complexity of games Helly metric Multi-agent system PPAD-complete Mathematics portal Game theory WikiProject
Aspiration_window
American economist (born 1950)
Bertrand paradox Chainstore paradox Computational complexity of games Helly metric Multi-agent system PPAD-complete Mathematics portal Game theory WikiProject
David_M._Kreps
Level of information in economics and game theory
Bertrand paradox Chainstore paradox Computational complexity of games Helly metric Multi-agent system PPAD-complete Mathematics portal Game theory WikiProject
Complete_information
When a decision-maker's future preferences can contradict earlier preferences
Bertrand paradox Chainstore paradox Computational complexity of games Helly metric Multi-agent system PPAD-complete Mathematics portal Game theory WikiProject
Dynamic_inconsistency
Economic model of competition
Bertrand paradox Chainstore paradox Computational complexity of games Helly metric Multi-agent system PPAD-complete Mathematics portal Game theory WikiProject
Bertrand_competition
Academic discipline
Bertrand paradox Chainstore paradox Computational complexity of games Helly metric Multi-agent system PPAD-complete Mathematics portal Game theory WikiProject
Quantum_game_theory
Model of humans as rational, self-interested agents
Bertrand paradox Chainstore paradox Computational complexity of games Helly metric Multi-agent system PPAD-complete Mathematics portal Game theory WikiProject
Homo_economicus
Class of strategies employed in a repeated non-cooperative game
Bertrand paradox Chainstore paradox Computational complexity of games Helly metric Multi-agent system PPAD-complete Mathematics portal Game theory WikiProject
Trigger_strategy
Subset of a game; used in game theory
Bertrand paradox Chainstore paradox Computational complexity of games Helly metric Multi-agent system PPAD-complete Mathematics portal Game theory WikiProject
Subgame
Israeli-American psychologist and economist (1934–2024)
Bertrand paradox Chainstore paradox Computational complexity of games Helly metric Multi-agent system PPAD-complete Mathematics portal Game theory WikiProject
Daniel_Kahneman
Concept in game theory
Bertrand paradox Chainstore paradox Computational complexity of games Helly metric Multi-agent system PPAD-complete Mathematics portal Game theory WikiProject
Non-credible_threat
Algorithmically defined graph
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
Implicit_graph
Generalization of the normal-form game
in a concave game is PPAD-complete. In fact, they prove that the problem is in PPAD even for general concave games, and it is PPAD-hard even in the special
Concave_game
Solution concept in game theory
Bertrand paradox Chainstore paradox Computational complexity of games Helly metric Multi-agent system PPAD-complete Mathematics portal Game theory WikiProject
Evolutionarily stable strategy
Evolutionarily_stable_strategy
Iterated game for peace and conflict studies
Bertrand paradox Chainstore paradox Computational complexity of games Helly metric Multi-agent system PPAD-complete Mathematics portal Game theory WikiProject
Peace_war_game
Conflict between safety and cooperation
Bertrand paradox Chainstore paradox Computational complexity of games Helly metric Multi-agent system PPAD-complete Mathematics portal Game theory WikiProject
Stag_hunt
2023-04-23. Burguillo, Juan C. (2018). Self-organizing coalitions for managing complexity : agent-based simulation of evolutionary game theory models using dynamic
Outcome_(game_theory)
Argument in combinatorial game theory
Bertrand paradox Chainstore paradox Computational complexity of games Helly metric Multi-agent system PPAD-complete Mathematics portal Game theory WikiProject
Strategy-stealing_argument
Solution concept in game theory
Bertrand paradox Chainstore paradox Computational complexity of games Helly metric Multi-agent system PPAD-complete Mathematics portal Game theory WikiProject
Quantal_response_equilibrium
Statement that players know and also know that other players know (ad infinitum)
Bertrand paradox Chainstore paradox Computational complexity of games Helly metric Multi-agent system PPAD-complete Mathematics portal Game theory WikiProject
Common_knowledge_(logic)
Concept in game theory
Bertrand paradox Chainstore paradox Computational complexity of games Helly metric Multi-agent system PPAD-complete Mathematics portal Game theory WikiProject
Best_response
one another. This flexibility introduces unique strategic dynamics and complexities to the study of decision-making in such environments. For example, in
Asynchrony_(game_theory)
Bertrand paradox Chainstore paradox Computational complexity of games Helly metric Multi-agent system PPAD-complete Mathematics portal Game theory WikiProject
Implementation_theory
Game in economic experiments
Bertrand paradox Chainstore paradox Computational complexity of games Helly metric Multi-agent system PPAD-complete Mathematics portal Game theory WikiProject
Ultimatum_game
Bertrand paradox Chainstore paradox Computational complexity of games Helly metric Multi-agent system PPAD-complete Mathematics portal Game theory WikiProject
Transferable_utility
Modelling evolution using differential equations
Bertrand paradox Chainstore paradox Computational complexity of games Helly metric Multi-agent system PPAD-complete Mathematics portal Game theory WikiProject
Evolutionary_dynamics
Simultaneous game found in game theory
Bertrand paradox Chainstore paradox Computational complexity of games Helly metric Multi-agent system PPAD-complete Mathematics portal Game theory WikiProject
Coordination_game
Concept in economics and game theory
Bertrand paradox Chainstore paradox Computational complexity of games Helly metric Multi-agent system PPAD-complete Mathematics portal Game theory WikiProject
Price_of_anarchy
Game illustrating paradox in rational choice theory
Bertrand paradox Chainstore paradox Computational complexity of games Helly metric Multi-agent system PPAD-complete Mathematics portal Game theory WikiProject
Dollar_auction
Bertrand paradox Chainstore paradox Computational complexity of games Helly metric Multi-agent system PPAD-complete Mathematics portal Game theory WikiProject
Uncorrelated_asymmetry
Problem in game theory
Bertrand paradox Chainstore paradox Computational complexity of games Helly metric Multi-agent system PPAD-complete Mathematics portal Game theory WikiProject
El_Farol_Bar_problem
Study of fair cake-cutting with true valuations
Bertrand paradox Chainstore paradox Computational complexity of games Helly metric Multi-agent system PPAD-complete Mathematics portal Game theory WikiProject
Truthful_cake-cutting
Dynamical system
Bertrand paradox Chainstore paradox Computational complexity of games Helly metric Multi-agent system PPAD-complete Mathematics portal Game theory WikiProject
Replicator_equation
Condition in economics and game theory
Bertrand paradox Chainstore paradox Computational complexity of games Helly metric Multi-agent system PPAD-complete Mathematics portal Game theory WikiProject
Perfect_information
travel, tourism, insurance
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travel, tourism, insurance