Semiring-based constraint satisfaction and optimization
Journal of the ACM (JACM)
Graphical Models for Game Theory
UAI '01 Proceedings of the 17th Conference in Uncertainty in Artificial Intelligence
Solving Non-binary CSPs Using the Hidden Variable Encoding
CP '01 Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming
Order independence and rationalizability
TARK '05 Proceedings of the 10th conference on Theoretical aspects of rationality and knowledge
A Comparison of the Notions of Optimality in Soft Constraints and Graphical Games
Recent Advances in Constraints
Constraint-based preferential optimization
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 1
Journal of Artificial Intelligence Research
Pure Nash equilibria: hard and easy games
Journal of Artificial Intelligence Research
Reasoning with conditional ceteris paribus preference statements
UAI'99 Proceedings of the Fifteenth conference on Uncertainty in artificial intelligence
Strategy elimination in games with interaction structures
LORI'09 Proceedings of the 2nd international conference on Logic, rationality and interaction
Distributed iterated elimination of strictly dominated strategies
Autonomous Agents and Multi-Agent Systems
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The notion of optimality naturally arises in many areas of applied mathematics and computer science concerned with decision making. Here we consider this notion in the context of three formalisms used for different purposes in reasoning about multi-agent systems: strategic games, CP-nets, and soft constraints. To relate the notions of optimality in these formalisms we introduce a natural qualitative modification of the notion of a strategic game. We show then that the optimal outcomes of a CP-net are exactly the Nash equilibria of such games. This allows us to use the techniques of game theory to search for optimal outcomes of CP-nets and vice-versa, to use techniques developed for CP-nets to search for Nash equilibria of the considered games. Then, we relate the notion of optimality used in the area of soft constraints to that used in a generalization of strategic games, called graphical games. In particular we prove that for a natural class of soft constraints that includes weighted constraints every optimal solution is both a Nash equilibrium and Pareto efficient joint strategy. For a natural mapping in the other direction we show that Pareto efficient joint strategies coincide with the optimal solutions of soft constraints.