  Whether in groups of humans or groups of computer agents, collaboration is
most effective between individuals who have the ability to coordinate on a
joint strategy for collective action. However, in general a rational actor will
only intend to coordinate if that actor believes the other group members have
the same intention. This circular dependence makes rational coordination
difficult in uncertain environments if communication between actors is
unreliable and no prior agreements have been made. An important normative
question with regard to coordination in these ad hoc settings is therefore how
one can come to believe that other actors will coordinate, and with regard to
systems involving humans, an important empirical question is how humans arrive
at these expectations. We introduce an exact algorithm for computing the
infinitely recursive hierarchy of graded beliefs required for rational
coordination in uncertain environments, and we introduce a novel mechanism for
multiagent coordination that uses it. Our algorithm is valid in any environment
with a finite state space, and extensions to certain countably infinite state
spaces are likely possible. We test our mechanism for multiagent coordination
as a model for human decisions in a simple coordination game using existing
experimental data. We then explore via simulations whether modeling humans in
this way may improve human-agent collaboration.
