From hierarchies to levels: new solutions for games with hierarchical structure

Autor: Gerard van der Laan, Mikel Álvarez-Mozos, René van den Brink, Oriol Tejada
Přispěvatelé: Econometrics and Operations Research, Tinbergen Institute, Universitat de Barcelona
Rok vydání: 2017
Předmět:
Statistics and Probability
Computer Science::Computer Science and Game Theory
Economics and Econometrics
Class (set theory)
Theoretical computer science
Computer science
Generalization
TU-game
Structure (category theory)
Set (abstract data type)
Mathematics (miscellaneous)
0502 economics and business
Shapley value
050207 economics
Hierarchical structure
Axiomes
Axiom
Game theory
Cooperative games (Mathematics)
050205 econometrics
Mathematics
Bondareva–Shapley theorem
Non-cooperative game
Axioms
05 social sciences
Stochastic game
ComputingMilieux_PERSONALCOMPUTING
TheoryofComputation_GENERAL
Cooperative game theory
hierarchical structure
levels structure
Shapley Value
axiomatization
Teoria de jocs
Levels structure
Jocs cooperatius (Matemàtica)
Axiomatization
Statistics
Probability and Uncertainty
Mathematical economics
Social Sciences (miscellaneous)
Zdroj: Álvarez-Mozos, M, van den Brink, R, van der Laan, G & Tejada, O 2017, ' From hierarchies to levels : new solutions for games with hierarchical structure ', International Journal of Game Theory, vol. 46, no. 4, pp. 1089-1113 . https://doi.org/10.1007/s00182-017-0572-z
International Journal of Game Theory, 46(4), 1089-1113. Springer Verlag
Dipòsit Digital de la UB
Universidad de Barcelona
Recercat. Dipósit de la Recerca de Catalunya
instname
ISSN: 1432-1270
0020-7276
DOI: 10.1007/s00182-017-0572-z
Popis: Recently, applications of cooperative game theory to economic allocation problems have gained popularity. In many of these problems, players are organized according to either a hierarchical structure or a levels structure that restrict players’ possibilities to cooperate. In this paper, we propose three new solutions for games with hierarchical structure and characterize them by properties that relate a player’s payoff to the payoffs of other players located in specific positions in the structure relative to that player. To define each of these solutions, we consider a certain mapping that transforms any hierarchical structure into a levels structure, and then we apply the standard generalization of the Shapley Value to the class of games with levels structure. The transformations that map the set of hierarchical structures to the set of levels structures are also studied from an axiomatic viewpoint by means of properties that relate a player’s position in both types of structure.
Databáze: OpenAIRE
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