Journal of Computer and System Sciences - 26th IEEE Conference on Foundations of Computer Science, October 21-23, 1985
Some algebraic and geometric computations in PSPACE
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Exponential lower bounds for finding Brouwer fixed points
Journal of Complexity
Simple local search problems that are hard to solve
SIAM Journal on Computing
Machine models and simulations
Handbook of theoretical computer science (vol. A)
Tree automata, Mu-Calculus and determinacy
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Journal of Symbolic Computation
A problem that is easier to solve on the unit-cost algebraic RAM
Journal of Complexity
The complexity of stochastic games
Information and Computation
On the complexity of the parity argument and other inefficient proofs of existence
Journal of Computer and System Sciences - Special issue: 31st IEEE conference on foundations of computer science, Oct. 22–24, 1990
Computational complexity of fixed points and intersection points
Journal of Complexity
The complexity of mean payoff games on graphs
Theoretical Computer Science
Theory of hybrid systems and discrete event systems
Theory of hybrid systems and discrete event systems
Competitive Markov decision processes
Competitive Markov decision processes
Complexity and real computation
Complexity and real computation
Deciding the winner in parity games is in UP ∩ co-UP
Information Processing Letters
Foundations of statistical natural language processing
Foundations of statistical natural language processing
Optimal solution of nonlinear equations
Optimal solution of nonlinear equations
The Analysis of Local Search Problems and Their Heuristics
STACS '90 Proceedings of the 7th Annual Symposium on Theoretical Aspects of Computer Science
Playing large games using simple strategies
Proceedings of the 4th ACM conference on Electronic commerce
Some NP-complete geometric problems
STOC '76 Proceedings of the eighth annual ACM symposium on Theory of computing
The complexity of pure Nash equilibria
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Model Checking Probabilistic Pushdown Automata
LICS '04 Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science
On algorithms for discrete and approximate brouwer fixed points
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
The complexity of computing a Nash equilibrium
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
On the Complexity of Numerical Analysis
CCC '06 Proceedings of the 21st Annual IEEE Conference on Computational Complexity
Settling the Complexity of Two-Player Nash Equilibrium
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Computing Nash Equilibria: Approximation and Smoothed Complexity
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
On the Impact of Combinatorial Structure on Congestion Games
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
The NP-completeness column: Finding needles in haystacks
ACM Transactions on Algorithms (TALG)
Progress in approximate nash equilibria
Proceedings of the 8th ACM conference on Electronic commerce
The approximation complexity of win-lose games
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Algorithmic Game Theory
On the Complexity of Nash Equilibria and Other Fixed Points (Extended Abstract)
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Inapproximability of pure nash equilibria
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Quasi-Birth-Death Processes, Tree-Like QBDs, Probabilistic 1-Counter Automata, and Pushdown Systems
QEST '08 Proceedings of the 2008 Fifth International Conference on Quantitative Evaluation of Systems
The complexity of equilibria: Hardness results for economies via a correspondence with games
Theoretical Computer Science
Recursive Markov chains, stochastic grammars, and monotone systems of nonlinear equations
Journal of the ACM (JACM)
Approximate Equilibria for Strategic Two Person Games
SAGT '08 Proceedings of the 1st International Symposium on Algorithmic Game Theory
Computational Aspects of Equilibria
SAGT '09 Proceedings of the 2nd International Symposium on Algorithmic Game Theory
Local search: simple, successful, but sometimes sluggish
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
On the complexity of core, kernel, and bargaining set
Artificial Intelligence
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Many models from a variety of areas involve the computation of an equilibrium or fixed point of some kind. Examples include Nash equilibria in games; market equilibria; computing optimal strategies and the values of competitive games (stochastic and other games); stable configurations of neural networks; analysing basic stochastic models for evolution like branching processes and for language like stochastic context-free grammars; and models that incorporate the basic primitives of probability and recursion like recursive Markov chains. It is not known whether these problems can be solved in polynomial time. There are certain common computational principles underlying different types of equilibria, which are captured by the complexity classes PLS, PPAD, and FIXP. Representative complete problems for these classes are, respectively, pure Nash equilibria in games where they are guaranteed to exist, (mixed) Nash equilibria in two-player normal form games, and (mixed) Nash equilibria in normal form games with three (or more) players. This paper reviews the underlying computational principles and the corresponding classes.