Symmetric Solutions of Some Production Economies
Sergiu Hart
Abstract
A symmetric n-person game (n,k) (for positive integer
k) is defined in its characteristic function form by
v(S) = [|S|]/k,
where |S| is the number of players
in the coalition S and [x]
denotes the largest integer not greater than x
(i.e., any k players, but not less, can
"produce" one unit). It is proved
that in any imputation in any symmetric von Neumann - Morgenstern solution of
such a game, a blocking coalition
of p = n-k+1 players who receive the largest
payoffs is formed, and their payoffs are always equal.
Conditions for existence and uniqueness of such symmetric solutions with the
other k-1 payoffs equal too are proved;
other cases are discussed thereafter.
- International Journal of Game Theory 2 (1973), 1, 53-62