Pro-Cooperative Games
Related to the display charts we are presenting is a concept
of "pro-cooperative games".
From the viewpoint of evolution (like in Nature) there could be
circumstances where three species of animals (or plants) might
naturally, in a particular localized environmental location, find only
one natural equilibrium mode of existence.
But on the other hand, in a different localized environment (or with
different species) there might naturally be more than one stable
equilibrium.
Our analogous observation with the three-party "cooperative" games
that we are studying (described by a characteristic function with b1,
b2, and b3 representing v(2,3), v{1,3), and v(1,2)) is that if b1, b2,
and b3 are all small that then it is natural for there to be only an
unique "central" equilibrium of cooperation (or of "bargaining" or
negotiation) but that if b1, b2, and b3 were all with slightly different
sizes but all near in size to 3/4 then that it would seem to be entirely
natural for there to be three distinct possibilities for a stable
equilibrium (as if under evolution). That is, any pair of the players
could have a stable alliance excluding the outside player and the
members of this pair of players could be allocating to each of
themselves at least 3/8 of the total game resources (and thus more than
a comparative quota of 1/3).
And, at least in part, it was learning, in a seminar, of Prof.
Maskin's concept of "externalities" as affecting the outcomes of games
otherwise described by a characteristic function that stimulated me to
think of this idea of circumstances that would modify an effective game
context. So I arrived at the concept of some games being distinguishable
as of "pro-cooperative" type.
But I must cautiously remark here that I DO NOT have a PRECISE
concept of a difference between pro-cooperative games and those not of
that type. But if we have any specific modeling of the games in terms of
a repeated games equilibrium then there could be values of b1, b2, and
b3 for which the equilibrium would be unique and other values for which
it would be non-unique and this phenomenon could be viewed as
corresponding to the concept or issue of pro-cooperative games.