Modal Logics of Negotiation and Preference
Ulle Endriss, Eric Pacuit

Abstract:
We develop a dynamic modal logic that can be used to model scenarios
where agents negotiate over the allocation of a finite number of
indivisible resources. The logic includes operators to speak about
both preferences of individual agents and deals regarding the
reallocation of certain resources. We reconstruct a known result
regarding the convergence of sequences of mutually beneficial deals to
a Pareto optimal allocation of resources, and discuss the relationship
between reasoning tasks in our logic and problems in negotiation. For
instance, checking whether a given restricted class of deals is
sufficient to guarantee convergence to a Pareto optimal allocation for
a specific negotiation scenario amounts to a model checking problem;
and the problem of identifying conditions on preference relations that
would guarantee convergence for a restricted class of deals under all
circumstances can be cast as a question in modal logic correspondence
theory.

Keywords: Modal Logic; Negotiation; Multiagent Resource Allocation;
  Social Software; Preference Representation