Contextual Coalitional Games

The study of cooperation among agents is of central interest in multiagent systems research. A popular way to model cooperation is through coalitional game theory. Much research in this area has had limited practical applicability as regards real-world multi-agent systems due to the fact that it assumes deterministic payoffs to coalitions and in addition does not apply to multi-agent environments that are stochastic in nature. In this paper, we propose a novel approach to modeling such scenarios where coalitional games will be contextualized through the use of logical expressions representing environmental and other state, and probability distributions will be placed on the space of contexts in order to model the stochastic nature of the scenarios. More formally, we present a formal representation language for representing contextualized coalitional games embedded in stochastic environments and we define and show how to compute expected Shapley values in such games in a computationally efficient manner. We present the value of the approach through an example involving robotics assistance in emergencies.