TY - JOUR

T1 - Set-valued capacities

T2 - multi-agenda decision making

AU - Lehrer, Ehud

AU - Teper, Roee

N1 - Publisher Copyright:
© 2018, Springer-Verlag GmbH Germany, part of Springer Nature.

PY - 2020/2/1

Y1 - 2020/2/1

N2 - We study the problem in which a set of agents are required to produce across several different projects (or more generally, agendas), and we consider environments in which resources are constrained and investing (say, time or effort) in one agenda reduces the ability to invest in other agendas. To this end, we introduce a class of capacities we refer to as set-valued: the value of each coalition is a subset of a vector space. For a particular coalition, each vector in its value is associated with a different distribution of the resources invested across the different agendas. In this context, the Choquet and the concave integrals are defined, characterized and shown to be identical if and only if the underlying set-valued capacity is supermodular. We apply the tools developed and introduce a new decision theory.

AB - We study the problem in which a set of agents are required to produce across several different projects (or more generally, agendas), and we consider environments in which resources are constrained and investing (say, time or effort) in one agenda reduces the ability to invest in other agendas. To this end, we introduce a class of capacities we refer to as set-valued: the value of each coalition is a subset of a vector space. For a particular coalition, each vector in its value is associated with a different distribution of the resources invested across the different agendas. In this context, the Choquet and the concave integrals are defined, characterized and shown to be identical if and only if the underlying set-valued capacity is supermodular. We apply the tools developed and introduce a new decision theory.

KW - Choquet integral

KW - Concave integral

KW - Set-valued capacities

KW - Supermodular set-valued games

UR - http://www.scopus.com/inward/record.url?scp=85057948030&partnerID=8YFLogxK

U2 - 10.1007/s00199-018-1164-2

DO - 10.1007/s00199-018-1164-2

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AN - SCOPUS:85057948030

SN - 0938-2259

VL - 69

SP - 233

EP - 248

JO - Economic Theory

JF - Economic Theory

IS - 1

ER -