A catalog of complexity classes
Handbook of theoretical computer science (vol. A)
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 selecting maximal solutions
Information and Computation
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
On the Desirability of Acyclic Database Schemes
Journal of the ACM (JACM)
Constraint satisfaction and database theory: a tutorial
PODS '00 Proceedings of the nineteenth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
A comparison of structural CSP decomposition methods
Artificial Intelligence
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
The complexity of acyclic conjunctive queries
Journal of the ACM (JACM)
Tight bounds for worst-case equilibria
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Theoretical Computer Science
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
The Structure and Complexity of Nash Equilibria for a Selfish Routing Game
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
UAI '00 Proceedings of the 16th Conference on Uncertainty in Artificial Intelligence
Graphical Models for Game Theory
UAI '01 Proceedings of the 17th Conference in Uncertainty in Artificial Intelligence
Multi-agent algorithms for solving graphical games
Eighteenth national conference on Artificial intelligence
The complexity of pure Nash equilibria
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Reasoning about Rationality and Beliefs
AAMAS '04 Proceedings of the Third International Joint Conference on Autonomous Agents and Multiagent Systems - Volume 2
Computing Nash equilibria of action-graph games
UAI '04 Proceedings of the 20th conference on Uncertainty in artificial intelligence
Reducibility among equilibrium problems
Proceedings of the thirty-eighth 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
Nash equilibria in graphical games on trees revisited
EC '06 Proceedings of the 7th ACM conference on Electronic commerce
The computational complexity of nash equilibria in concisely represented games
EC '06 Proceedings of the 7th ACM conference on Electronic commerce
Structure and complexity of extreme Nash equilibria
Theoretical Computer Science - Game theory meets theoretical computer science
Settling the Complexity of Two-Player Nash Equilibrium
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
On the structure and complexity of worst-case equilibria
Theoretical Computer Science
Computing good nash equilibria in graphical games
Proceedings of the 8th ACM conference on Electronic commerce
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
Pure Nash equilibria: hard and easy games
Journal of Artificial Intelligence Research
A continuation method for Nash equilibria in structured games
Journal of Artificial Intelligence Research
Complexity results about Nash equilibria
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
Efficient nash computation in large population games with bounded influence
UAI'02 Proceedings of the Eighteenth conference on Uncertainty in artificial intelligence
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A widely accepted rational behavior for non-cooperative players is based on the notion of Nash equilibrium. Although the existence of a Nash equilibrium is guaranteed in the mixed framework (i.e., when players select their actions in a randomized manner) in many real-world applications the existence of ''any'' equilibrium is not enough. Rather, it is often desirable to single out equilibria satisfying some additional requirements (in order, for instance, to guarantee a minimum payoff to certain players), which we call constrained Nash equilibria. In this paper, a formal framework for specifying these kinds of requirement is introduced and investigated in the context of graphical games, where a player p may directly be interested in some of the other players only, called the neighbors of p. This setting is very useful for modeling large population games, where typically each player does not directly depend on all the players, and representing her utility function extensively is either inconvenient or infeasible. Based on this framework, the complexity of deciding the existence and of computing constrained equilibria is then investigated, in the light of evidencing how the intrinsic difficulty of these tasks is affected by the requirements prescribed at the equilibrium and by the structure of players' interactions. The analysis is carried out for the setting of mixed strategies as well as for the setting of pure strategies, i.e., when players are forced to deterministically choose the action to perform. In particular, for this latter case, restrictions on players' interactions and on constraints are identified, that make the computation of Nash equilibria an easy problem, for which polynomial and highly-parallelizable algorithms are presented.