Long-term implementation of the cooperative solution in a multistage multicriteria game

Research output

1 Citation (Scopus)

Abstract

In order to find an optimal and time consistent cooperative path in multicriteria multistage game the minimal sum of relative deviations rule is introduced. Using this rule one can construct a vector-valued characteristic function that is weakly superadditive. The sustainability of the cooperative agreement is ensured by using an imputation distribution procedure (IDP) based approach. We formulate the conditions an IDP should satisfy to guarantee that the core is strongly time consistent (STC). Namely, if the imputation distribution procedure for the Shapley value satisfies the efficiency condition, the strict balance condition and the strong irrational-behavior-proof condition, given that the Shapley value belongs to the core of each subgame along the cooperative path, it can be used as a “supporting imputation” which guarantees that the whole core is STC. We discuss three payment schedules and check whether they can be used as supporting imputation distribution procedures for the considered multicriteria game.

Original languageEnglish
Article number100107
JournalOperations Research Perspectives
Volume6
DOIs
Publication statusPublished - 1 Jan 2019

Fingerprint

Multicriteria Games
Imputation
Shapley Value
Path
Vector-valued Functions
Sustainability
Multi-criteria
Characteristic Function
Schedule
Deviation
Cooperative solution
Game

Scopus subject areas

  • Statistics and Probability
  • Strategy and Management
  • Control and Optimization
  • Management Science and Operations Research

Cite this

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title = "Long-term implementation of the cooperative solution in a multistage multicriteria game",
abstract = "In order to find an optimal and time consistent cooperative path in multicriteria multistage game the minimal sum of relative deviations rule is introduced. Using this rule one can construct a vector-valued characteristic function that is weakly superadditive. The sustainability of the cooperative agreement is ensured by using an imputation distribution procedure (IDP) based approach. We formulate the conditions an IDP should satisfy to guarantee that the core is strongly time consistent (STC). Namely, if the imputation distribution procedure for the Shapley value satisfies the efficiency condition, the strict balance condition and the strong irrational-behavior-proof condition, given that the Shapley value belongs to the core of each subgame along the cooperative path, it can be used as a “supporting imputation” which guarantees that the whole core is STC. We discuss three payment schedules and check whether they can be used as supporting imputation distribution procedures for the considered multicriteria game.",
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KW - Dynamic game

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