TY - JOUR
T1 - Values of mixed games
AU - Hart, Sergiu
PY - 1973/12
Y1 - 1973/12
N2 - Aumann and Shapley [1973] have investigated values of games in which all players are individually insignificant, i.e. form a non-atomic continuum, or "ocean". In this paper we treat games in which, in addition to such an ocean, there are also some "atoms", i.e. players who are individually significant. We define spaces of such games that are analogous to those investigated by Aumann and Shapley, and prove the existence of values on some of them. Unlike in the non-atomic case, we find that in general there are infinitely many values, corresponding to various ways in which the atoms can be imbedded in the ocean. The results generalize those of Milnor and Shapley [1961]. Precise statements will be found in Section 2.
AB - Aumann and Shapley [1973] have investigated values of games in which all players are individually insignificant, i.e. form a non-atomic continuum, or "ocean". In this paper we treat games in which, in addition to such an ocean, there are also some "atoms", i.e. players who are individually significant. We define spaces of such games that are analogous to those investigated by Aumann and Shapley, and prove the existence of values on some of them. Unlike in the non-atomic case, we find that in general there are infinitely many values, corresponding to various ways in which the atoms can be imbedded in the ocean. The results generalize those of Milnor and Shapley [1961]. Precise statements will be found in Section 2.
UR - http://www.scopus.com/inward/record.url?scp=0343424083&partnerID=8YFLogxK
U2 - 10.1007/BF01737560
DO - 10.1007/BF01737560
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:0343424083
SN - 0020-7276
VL - 2
SP - 69
EP - 85
JO - International Journal of Game Theory
JF - International Journal of Game Theory
IS - 1
ER -