The Intermediate Set and Limiting Superdi erential for Coalition Games: Between the Core and the Weber Set
Result description
We introduce the intermediate set as an interpolating solution concept between the core and the Weber set of a coalitional game. The new solution is de ned as the limiting superdi erential of the Lov asz extension and thus it completes the hierarchy of variational objects used to represent the core (Fr echet superdi erential) and the Weber set (Clarke superdi erential). It is shown that the intermediate set is a non-convex solution containing the Pareto optimal payo vectors that depend on some chain of coalitions and marginal coalitional contributions with respect to the chain. A detailed comparison between the intermediate set and other set-valued solutions is provided. We compute the exact form of intermediate set for all games and provide its simpli ed characterization for the simple games and the glove game.
Keywords
coalition gamelimiting superdi erentialintermediate setcoreWeber set
The result's identifiers
Result code in IS VaVaI
Result on the web
DOI - Digital Object Identifier
Alternative languages
Result language
angličtina
Original language name
The Intermediate Set and Limiting Superdi erential for Coalition Games: Between the Core and the Weber Set
Original language description
We introduce the intermediate set as an interpolating solution concept between the core and the Weber set of a coalitional game. The new solution is de ned as the limiting superdi erential of the Lov asz extension and thus it completes the hierarchy of variational objects used to represent the core (Fr echet superdi erential) and the Weber set (Clarke superdi erential). It is shown that the intermediate set is a non-convex solution containing the Pareto optimal payo vectors that depend on some chain of coalitions and marginal coalitional contributions with respect to the chain. A detailed comparison between the intermediate set and other set-valued solutions is provided. We compute the exact form of intermediate set for all games and provide its simpli ed characterization for the simple games and the glove game.
Czech name
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Czech description
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Classification
Type
Jimp - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10103 - Statistics and probability
Result continuities
Project
GA15-00735S: Stability analysis of optima and equilibria in economics
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
International Journal of Game Theory
ISSN
0020-7276
e-ISSN
—
Volume of the periodical
46
Issue of the periodical within the volume
4
Country of publishing house
CH - SWITZERLAND
Number of pages
28
Pages from-to
891-918
UT code for WoS article
000413759000001
EID of the result in the Scopus database
2-s2.0-84997171421
Basic information
Result type
Jimp - Article in a specialist periodical, which is included in the Web of Science database
OECD FORD
Statistics and probability
Year of implementation
2017