On three Shapley-like solutions for cooperative games with random payoffs

Judith B. Timmer; Peter Borm; Stef Tijs

doi:10.1007/s001820400181

On three Shapley-like solutions for cooperative games with random payoffs

Judith B. Timmer, Peter Borm, Stef Tijs

Stochastic Operations Research

Research output: Contribution to journal › Article › Academic › peer-review

27 Citations (Scopus)

1 Downloads (Pure)

Abstract

Three solution concepts for cooperative games with random payoffs are introduced. These are the marginal value, the dividend value and the selector value. Inspiration for their definitions comes from several equivalent formulations of the Shapley value for cooperative TU games. An example shows that the equivalence is not preserved since these solutions can all be different for cooperative games with random payoffs. Properties are studied and a characterization on a subclass of games is provided.

Original language	Undefined
Pages (from-to)	595-613
Number of pages	19
Journal	International journal of game theory
Volume	32
Issue number	4
DOIs	https://doi.org/10.1007/s001820400181
Publication status	Published - Aug 2004

Keywords

Cooperative games - Random variables - Shapley value
Shapley value
random variables
EWI-17803
MSC-91A12
METIS-220442
IR-58681
Cooperative games

Access to Document

10.1007/s001820400181

http://eprints.eemcs.utwente.nl/secure2/17803/01/2003-35TimmerBormTijs.pdf

Cite this

@article{a42cdd366a84426fb3912f839f796628,

title = "On three Shapley-like solutions for cooperative games with random payoffs",

abstract = "Three solution concepts for cooperative games with random payoffs are introduced. These are the marginal value, the dividend value and the selector value. Inspiration for their definitions comes from several equivalent formulations of the Shapley value for cooperative TU games. An example shows that the equivalence is not preserved since these solutions can all be different for cooperative games with random payoffs. Properties are studied and a characterization on a subclass of games is provided.",

keywords = "Cooperative games - Random variables - Shapley value, Shapley value, random variables, EWI-17803, MSC-91A12, METIS-220442, IR-58681, Cooperative games",

author = "Timmer, {Judith B.} and Peter Borm and Stef Tijs",

note = "This author acknowledges financial support from the Netherlands Organization for Scientific Research (NWO) through project 613-304-059.",

year = "2004",

month = aug,

doi = "10.1007/s001820400181",

language = "Undefined",

volume = "32",

pages = "595--613",

journal = "International journal of game theory",

issn = "0020-7276",

publisher = "Springer",

number = "4",

}

TY - JOUR

T1 - On three Shapley-like solutions for cooperative games with random payoffs

AU - Timmer, Judith B.

AU - Borm, Peter

AU - Tijs, Stef

N1 - This author acknowledges financial support from the Netherlands Organization for Scientific Research (NWO) through project 613-304-059.

PY - 2004/8

Y1 - 2004/8

N2 - Three solution concepts for cooperative games with random payoffs are introduced. These are the marginal value, the dividend value and the selector value. Inspiration for their definitions comes from several equivalent formulations of the Shapley value for cooperative TU games. An example shows that the equivalence is not preserved since these solutions can all be different for cooperative games with random payoffs. Properties are studied and a characterization on a subclass of games is provided.

AB - Three solution concepts for cooperative games with random payoffs are introduced. These are the marginal value, the dividend value and the selector value. Inspiration for their definitions comes from several equivalent formulations of the Shapley value for cooperative TU games. An example shows that the equivalence is not preserved since these solutions can all be different for cooperative games with random payoffs. Properties are studied and a characterization on a subclass of games is provided.

KW - Cooperative games - Random variables - Shapley value

KW - Shapley value

KW - random variables

KW - EWI-17803

KW - MSC-91A12

KW - METIS-220442

KW - IR-58681

KW - Cooperative games

U2 - 10.1007/s001820400181

DO - 10.1007/s001820400181

M3 - Article

SN - 0020-7276

VL - 32

SP - 595

EP - 613

JO - International journal of game theory

JF - International journal of game theory

IS - 4

ER -