The equal split-off set for cooperative games

Brânzei, R.; Dimitrov, Dinko; Tijs, S.H.

doi:10.4064/bc71-0-3

Cited by 46 publications

(45 citation statements)

References 4 publications

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“…The most widespread methods for pay-off allocation in cooperative game theory are the Shapley value and the τ -value [16]. In this paper, transmission active and reactive loss allocation of bilateral transactions simultaneously using cooperative game theory concepts and load flow studies is presented.…”

Section: Introductionmentioning

confidence: 99%

Active and reactive power transmission loss allocation to bilateral contracts through game theory techniques

Nafisi¹,

Roudsari²,

Hosseinian³

et al. 2015

Turk J Elec Eng & Comp Sci

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Transmission loss has a considerable effect in overall power generation. For fairly distributing the charge of losses to generators and consumers in a deregulated power system, the allocation of this loss is very important. Gametheoretic methods seem fairer for share determination of each participant of a coalition with no discrimination. In this paper, the active and reactive power transmission losses are allocated to bilateral transactions simultaneously through load flow calculations and cooperative game theory solutions. The loss allocation problem and each bilateral transaction are treated as a game and a player of the game, correspondingly. Two game theory-based approaches, the Shapley value and the τ -value, are surveyed. The former is the most relevant game theory allocation method, while the latter is a novel approach. The influences of all loss allocation game players and bilateral bargains on transmission loss are considered.These two proposed methods are applied to a simple 6-bus network and the modified IEEE 57-bus test system. In the 6-bus network positive MVA loss allocations and in the IEEE 57-bus system negative MVA loss allocations are studied.Finally, the results of allocation procedures are compared to each other.

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Section: Introductionmentioning

confidence: 99%

Active and reactive power transmission loss allocation to bilateral contracts through game theory techniques

Nafisi¹,

Roudsari²,

Hosseinian³

et al. 2015

Turk J Elec Eng & Comp Sci

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“…Comprehensive sources on classical cooperative game theory are for example [11] [14] [15] [18]. For more information on applications, see e.g.…”

Section: Classical Cooperative Game Theorymentioning

confidence: 99%

Selection-based Approach to Cooperative Interval Games

Bok

Hladík

2015

Proceedings of the International Conference on Operations Research and Enterprise Systems

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Abstract. Cooperative interval games are a generalized model of cooperative games in which the worth of every coalition corresponds to a closed interval representing the possible outcomes of its cooperation. Selections are all possible outcomes of the interval game with no additional uncertainty. We introduce new selection-based classes of interval games and prove their characterization theorems and relations to existing classes based on the interval weakly better operator. We show new results regarding the core and imputations and examine a problem of equivalence between two different versions of the core, which is the main stability solution of cooperative games. Then we introduce the definition of strong imputation and strong core as a universal solution concept of interval games.

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“…The equal split-off set [3] of a subadditive cooperative game (N, c) is the set of all cost allocations that can be computed by the following algorithm, again, inspired by the algorithm of Dutta and Ray [8]. (Note that Branzei et al [3] define the equal split-off set for superadditive reward cooperative games. Here, we look at the natural equivalent for cost cooperative games.)…”

Section: Lemma 32mentioning

confidence: 99%

“…The construction used in the proof of this result implies that computing the prices output by egalitarian mechanisms is NP-hard. This construction also has implications on the computational complexity of the equal split-off set [3] of linear programming games.…”

Section: Introductionmentioning

confidence: 99%