Journal of Computer and System Sciences - 26th IEEE Conference on Foundations of Computer Science, October 21-23, 1985
Exponential lower bounds for finding Brouwer fixed points
Journal of Complexity
Tree automata, Mu-Calculus and determinacy
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
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
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
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
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
A characterization of the class of functions computable in polynomial time on Random Access Machines
STOC '81 Proceedings of the thirteenth 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
The complexity of computing a Nash equilibrium
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
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
Fast-converging tatonnement algorithms for one-time and ongoing market problems
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Approximate Equilibria for Strategic Two Person Games
SAGT '08 Proceedings of the 1st International Symposium on Algorithmic Game Theory
Settling the complexity of computing two-player Nash equilibria
Journal of the ACM (JACM)
A Survey of Stochastic Games with Limsup and Liminf Objectives
ICALP '09 Proceedings of the 36th Internatilonal Collogquium on Automata, Languages and Programming: Part II
On the Complexity of Numerical Analysis
SIAM Journal on Computing
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Recursive concurrent stochastic games
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part II
Recursive markov decision processes and recursive stochastic games
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Survey: Equilibria, fixed points, and complexity classes
Computer Science Review
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Equilibria play a central role in game theory and economics. They characterize the possible outcomes in the interaction of rational, optimizing agents: In a game between rational players that want to optimize their payoffs, the only solutions in which no player has any incentive to switch his strategy are the Nash equilibria. Price equilibria in markets give the prices that allow the market to clear (demand matches supply) while the traders optimize their preferences (utilities). Fundamental theorems of Nash [34] and Arrow-Debreu [2] established the existence of the respective equilibria (under suitable conditions in the market case). The proofs in both cases use a fixed point theorem (relying ultimately on a compactness argument), and are non-constructive, i.e., do not yield an algorithm for constructing an equilibrium. We would clearly like to compute these predicted outcomes. This has led to extensive research since the 60's in the game theory and mathematical economics literature, with the development of several methods for computation of equilibria, and more generally fixed points. More recently, equilibria problems have been studied intensively in the computer science community, from the point of view of modern computation theory. While we still do not know definitely whether equilibria can be computed in general efficiently or not, these investigations have led to a better understanding of the computational complexity of equilibria, the various issues involved, and the relationship with other open problems in computation. In this talk we will discuss some of these aspects and our current understanding of the relevant problems. We outline below the main points and explain some of the related issues.