TY - JOUR
T1 - Symmetric solutions of some production economies
AU - Hart, Sergiu
PY - 1973/12
Y1 - 1973/12
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0038702638&partnerID=8YFLogxK
U2 - 10.1007/BF01737557
DO - 10.1007/BF01737557
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AN - SCOPUS:0038702638
SN - 0020-7276
VL - 2
SP - 53
EP - 62
JO - International Journal of Game Theory
JF - International Journal of Game Theory
IS - 1
ER -