FAX message to Prof. Lloyd S. Shapley 

  Depts. of Maths. and Econs., UCLA, West L.A., CA

  Fax #’s: 1-310-206-6673 and 1-310-825-9528
 
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Dear Lloyd,

         I am studying the references that you advised me of and what I can find. I want to be sure of what precisely Harsanyi used as a modified characteristic
function and of what it was called, etc.
    And coincidentally the 1964 paper by R. Selten in the Dresher-edited “Advances in ..” seems to use
the same phrase “modified Shapley value” that Harsanyi used first. I feel that I need to know,
simply in the case of transferable utility games,
whether or not they can be regarded as having used,
precisely, what I was calling the “HCF” or Harsanyi
characteristic function. I saw that Selten was using
the phrase “characteristic” rather than c. function.
           Now, if there is (as I have been thinking), a good argument for effectively arriving at this value
(modified Shapley value) for 3-person games WITHOUT
using an axiom or axioms of additivity/linearity then I observe that there seems to be a coincidental
analogy with very early (1928) Von Neumann argument
that was apparently pushed aside later when he, with
Morgenstern, got into the “stable sets”. In his first paper, as translated in the 4th Annals study,
He appears to have claimed a solvability for games
Of 2 or 3 players that DID NOT EXTEND to 4 players
Or more, and Kuhn was telling me that the idea there
was, indeed, an instance of Shapley value being
applied.
   I still need to find out precisely how Isbell was
able to effectively criticize Harsanyi’s first version.