Constrained core solutions for totally positive games with ordered players

Brink, René van den; Laan, Gerard van der; Васильев, В. А.

doi:10.1007/s00182-013-0382-x

Cited by 10 publications

(10 citation statements)

References 19 publications

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“…11 Proposition 3 shows, under the assumption of a uniform distribution, that the value of the transfer rate needed to implement the Expected Responsibility is higher than the one needed to implement the Median Responsibility. Since the responsibility functions are increasing and convex or decreasing and concave, one should analyze 11 In the case of the uniform distribution, we also have that med (C,t,t) (t) = E (C,t,t) (t) and, therefore, the median responsibility can be calculated with V i (E (C,t,t) (t), C). However, this equality may not occur with other distributions because the other arguments in the proof of Proposition 2 do not hold for all distributions.…”

Section: Discussionmentioning

confidence: 99%

Allocating the costs of cleaning a river: expected responsibility versus median responsibility

2020

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We consider the problem of cleaning a transboundary river, proposed by Ni and Wang (2007). A river is modeled as a segment divided into subsegments, each occupied by one region, from upstream to downstream. The waste is transferred from one region to the next at some rate. Since this transfer rate may be unknown, the social planner could have uncertainty over each region's responsibility. Two natural candidates to distribute the costs in this setting would be the method that assigns to each region its expected responsibility and the one that assigns to each region its median responsibility. We show that the latter is equivalent to the Upstream Responsibility method (Alcalde-Unzu et al., 2015) and the former is a new method that we call Expected Responsibility. We compare both solutions and analyze them in terms of a new property of monotonicity.

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Section: Discussionmentioning

confidence: 99%

Allocating the costs of cleaning a river: expected responsibility versus median responsibility

2020

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“…We now associate with each streaming problem (N, M, t) a T U game N, v (N,M,t) where the set of agents of the cooperative game is the set of artists. Given S ⊂ N we define v (N,M,t) (S) as the amount paid by the users that have only listened to artists in S. 15 Formally,…”

Section: A Game-theoretical Approachmentioning

confidence: 99%

Broadcasting revenue sharing after cancelling sports competitions

Bergantiños

Moreno‐Ternero

2023

Ann Oper Res

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The COVID-19 pandemic forced the partial or total cancellation of most sports competitions worldwide. Sports organizations crucially rely on revenues raised from broadcasting. How should the allocation of these revenues be modified when sports leagues are cancelled? We aim to answer that question in this paper by means of the axiomatic approach. Two extension operators (dubbed zero and leg operators, respectively) will play a major role in our analysis. We show that several combinations of axioms (formalizing ethical or strategic principles) characterize the image via those operators of two focal rules: the equal-split rule and concede-and-divide.

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“…To each game, the Conjunctive (Disjunctive) Permission Value assigns the Shapley Value of the conjunctive (disjunctive) permission restricted game. 1 More recently, van den Brink et al (2014) introduced another value for the class of games with permission structure where the TU-game is totally positive by restricting the allocation of dividends. In van den Brink et al (2015), a value for games with hierarchical structure has been proposed, the so-called Average Tree permission value.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2017

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in May 11, 2015Abstract 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.

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Constrained core solutions for totally positive games with ordered players

Cited by 10 publications

References 19 publications

Allocating the costs of cleaning a river: expected responsibility versus median responsibility

Allocating the costs of cleaning a river: expected responsibility versus median responsibility

Broadcasting revenue sharing after cancelling sports competitions

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

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