The concept of the next major research project,
in terms of mathematical efforts of calculation, is
that of studying again the same sort of three-person
games (of "bargaining and negotiation") but with
a model of agencies in which the "agents" will be
like attorneys of a robotic variety. The agents
will themselves play to maximize their income from 
fees, but this will be as if their cost (in fees) 
is truly infinitesimal and paid by "the state". 
   For this project it is very relevant that we
have made the operational discovery that a model
of negotiative bargaining can have "reluctant
acceptance behavior" on the part of the players.
   (We found with the form of modelling already
studied that the relevant equilibria would take
the form that the players would be playing so that
each would most often decline to accept another
player as his/her agent but instead wait and hope
to BE ACCEPTED as the empowered agent.) 
   (And this sort of behavior appears to make more 
easily feasible a variety of modelling in which an 
attorney agent will need, at the beginning of the
election of agencies, to be simultaneously elected
by two separate players (of the original set) in
order to become authorized/empowered to act as
their agent through the remainder of the process
of coalescence and the achievement of cooperation.)
   And another reason for this study choice is that
the results from the prior study indicated very
considerable divergence from the Shapley in terms
of the evaluation of the effective importance of
comparatively weak coalitions of two of the three
players. And there were also divergences, naturally, 
from the nucleolus, or the modiclus, if either of
those "imputation selectors" were to be taken as
a basis for an "evaluation" of a game.
   So the thought is that a different specific
form of modelling would probably offer at least
something analogous to a "second opinion" for use
in comparisons. And the case of games of three
players is itself so much an area that is really
not understood (to the extent that a good method
for arbitration of game-like situations could be
deduced) that it is not needed yet to study games
of four or more players to get into the areas of
comparative ignorance of good theory.