Expressivity and Complexity of Reasoning about Coalitional Interaction: Extended Abstract

This paper studies expressivity and complexity of normal modal logics for reasoning about coalitional power in multi-agent systems with agents that have preferences. A class of local and global notions relevant for reasoning about cooperation is identified. Many of these notions naturally correspond to concepts from game theory or social choice theory. The expressive power required to express the notions is determined via invariance results under various operations on different classes of Kripke models and frames. Our results apply to three different classes of models, each of them representing coalitional power from a slightly different perspective. One of these classes contains the models of a normal simulation of Pauly’s Coalition Logic. A large class of known extended modal languages is specified and we show how the chosen notions can be expressed in fragments of this class. To determine how demanding reasoning about cooperation is in terms of computational complexity, we use complexity results for extended modal logics and obtain for each local notion an upper bound on the complexity of modal logics expressing it.