Optimization, Games, and Quantified Constraint Satisfaction

Abstract Optimization problems considered in the literature generally assume a passive environment that does not react to the actions of an agent. In this paper, we introduce and study a class of optimization problems in which the environment plays an active, adversarial role and responds dynamically to the actions of an agent; this class of problems is based on the framework of quantified constraint satisfaction. We formalize a new notion of approximation algorithm for these optimization problems, and consider certain restricted versions of the general problem obtained by restricting the types of constraints that may appear. Our main result is a dichotomy theorem classifying exactly those restricted versions having a constant factor approximation algorithm.

Authors

• Hubie Chen
• Martin Pál

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