TY - JOUR

T1 - Large symmetric games are characterized by completeness of the desirability relation

AU - Einy, Ezra

AU - Neyman, Abraham

N1 - Funding Information:
This work was supported by the U.S. NSF Grant DMS 8705294 and Israel-US. Grant 8400201 and by CORE.

PY - 1989/1/1

Y1 - 1989/1/1

N2 - The paper presents a characterization of continuous cooperative games (set functions) which are monotonic functions of countably additive non-atomic measures. The characterization is done through a natural desirablity relation defined on the set of coalitions of players. A coalition S is at least as desirable as a coalition T (with respect to a given game υ (in colational form)), if for each coalition U that is disjoint from S ∪ T, υ(S ∪ U) ≥ υ(T ∪ U). The characterization asserts, that a game υ is of the form υ = f · μ, where μ is a non-atomic signed measure and f is a monotonic and continuous function on the range of μ, if, and only if, it is in pNA′ (i.e., it is a uniform limit of polynomials in non-atomic measures or equivalently it is uniformly continuous function in the NA-topology) and has a complete desirability relation.

AB - The paper presents a characterization of continuous cooperative games (set functions) which are monotonic functions of countably additive non-atomic measures. The characterization is done through a natural desirablity relation defined on the set of coalitions of players. A coalition S is at least as desirable as a coalition T (with respect to a given game υ (in colational form)), if for each coalition U that is disjoint from S ∪ T, υ(S ∪ U) ≥ υ(T ∪ U). The characterization asserts, that a game υ is of the form υ = f · μ, where μ is a non-atomic signed measure and f is a monotonic and continuous function on the range of μ, if, and only if, it is in pNA′ (i.e., it is a uniform limit of polynomials in non-atomic measures or equivalently it is uniformly continuous function in the NA-topology) and has a complete desirability relation.

UR - http://www.scopus.com/inward/record.url?scp=45249128825&partnerID=8YFLogxK

U2 - 10.1016/0022-0531(89)90033-1

DO - 10.1016/0022-0531(89)90033-1

M3 - Article

AN - SCOPUS:45249128825

VL - 48

SP - 369

EP - 385

JO - Journal of Economic Theory

JF - Journal of Economic Theory

SN - 0022-0531

IS - 2

ER -