Forbidding undesirable agreements: a dependence-based approach to the regulation of multi-agent systems

The purpose of this contribution is to set up a language to evaluate the results of concerted action among interdependent agents against predetermined properties that we can recognise as desirable from a deontic point of view. Unlike the standard view of logics to reason about coalitionally rational action, the capacity of a set of agents to take a rational decision will be restricted to what we will call agreements, that can be seen as solution concepts to a dependence structure present in a certain game. The language will identify in concise terms those agreements that act accordingly or disaccordingly with the desirable properties arbitrarily set up in the beginning, and will reveal, by logical reasoning, a variety of structural properties of this type of collective action.