Forbidding undesirable agreements

The purpose of this contribution1 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, which can be seen as solution concepts to a dependence structure present in a certain game. The language will identify 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.