ON THE COMPLEXITY OF COALITIONAL REASONING

Coalitional power in multistage processes is modeled using effectivity frames, which link an effectivity function to every possible state of the world. Effectivity frames are general enough to capture, e.g., what groups of agents can bring about in extensive games of perfect and almost perfect information. Coalition Logic is used to describe effectivity frames, and the question of generating an extensive game satisfying a given specification is formulated as a satisfiability problem in Coalition Logic. Using this logical reformulation, we show that the complexity of this implementation problem depends on two parameters: For coalitional specifications, the problem is shown to be PSPACE-complete. For individual specifications on the other hand, i.e., for specifications which only refer to the powers of individual agents, generating an implementation with perfect information is PSPACE-complete, whereas generating an implementation with almost perfect information is NP-complete.