Component efficient solutions in line-graph games with applications

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

doi:10.1007/s00199-006-0139-x

Cited by 57 publications

(27 citation statements)

References 27 publications

(31 reference statements)

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“…This assumption is driving the solution. Second, the solution by Ambec and Sprumont (2002) assigns all gains from cooperation to downstream agents which is not very convincing, as noted by Van den Brink et al (2007), Houba (2008) and Khmelnitskaya (2010).…”

Section: Constrained Direct Application Of Bankruptcy Rulesmentioning

confidence: 93%

Sequential sharing rules for river sharing problems

Ansink

Weikard

2011

Soc Choice Welf

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We analyse the redistribution of a resource amongst agents who have claims to the resource and who are ordered linearly. A well known example of this particular situation is the river sharing problem. We exploit the linear order of agents to transform the river sharing problem to a sequence of two-agent river sharing problems. These reduced problems are mathematically equivalent to bankruptcy problems and can therefore be solved using any bankruptcy rule. Our proposed class of solutions, that we call sequential sharing rules, solves the river sharing problem. Our approach extends the bankruptcy literature to settings with a sequential structure of both the agents and the resource to be shared. In the paper, we first characterise the class of sequential sharing rules. Subsequently, we apply sequential sharing rules based on four classical bankruptcy rules, assess their properties, provide two characterisations of one specific rule, and compare sequential sharing rules with three alternative solutions to the river sharing problem.

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Section: Constrained Direct Application Of Bankruptcy Rulesmentioning

confidence: 93%

Sequential sharing rules for river sharing problems

Ansink

Weikard

2011

Soc Choice Welf

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“…Another question for future research is to investigate axioms concerning changes in the parameters of the sequencing problem without changing the set of agents, such as the before mentioned balanced contributions property (Myerson 1980), fairness (Myerson 1977;van den Brink 2001) or monotonicity (Young 1985;van den Brink 2007).…”

Section: Discussionmentioning

confidence: 99%

Balanced consistency and balanced cost reduction for sequencing problems

Brink

Chun

2011

Soc Choice Welf

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We investigate the implications of balanced consistency and balanced cost reduction in the context of sequencing problems. Balanced consistency requires that the effect on the payoff from the departure of one agent to another agent should be equal between any two agents. On the other hand, balanced cost reduction requires that if one agent leaves a problem, then the total payoffs of the remaining agents should be affected by the amount previously assigned to the leaving agent. We show that the minimal transfer rule is the only rule satisfying efficiency and Pareto indifference together with either one of our two main axioms, balanced consistency and balanced cost reduction.

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“…We are interested in the class of Harsanyi solutions, introduced by Vasil'ev [21] for TU-games and studied by van den Brink et al [19] for communication situations. A Harsanyi solution distributes the Harsanyi dividends to the players of the corresponding coalitions according to a sharing function which assigns to each coalition S a sharing vector specifying for each player in S its share in the dividend of S. A sharing function on N is a function z which…”

Section: Communication Situationsmentioning

confidence: 99%

“…From this characterization, we obtain a useful expression of the average tree solution. This expression is used to show that the average tree solution with respect to T is a Harsanyi solution (see van den Brink et al [19]) if and only if T is a subset of the set introduced in [10].…”

Section: Introductionmentioning

confidence: 99%

Average tree solutions and the distribution of Harsanyi dividends

et al. 2010

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We consider communication situations games being the combination of a TU-game and a communication graph. We study the average tree (AT) solutions introduced by Herings et al. [9] and [10]. The AT solutions are defined with respect to a set, say T , of rooted spanning trees of the communication graph. We characterize these solutions by efficiency, linearity and an axiom of T -hierarchy. Then we prove the following results. Firstly, the AT solution with respect to T is a Harsanyi solution if and only if T is a subset of the set of trees introduced in [10]. Secondly, the latter set is constructed by the classical DFS algorithm and the associated AT solution coincides with the Shapley value when the communication graph is complete. Thirdly, the AT solution with respect to trees constructed by the other classical algorithm BFS yields the equal surplus division when the communication graph is complete.

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Component efficient solutions in line-graph games with applications

Cited by 57 publications

References 27 publications

Sequential sharing rules for river sharing problems

Sequential sharing rules for river sharing problems

Balanced consistency and balanced cost reduction for sequencing problems

Average tree solutions and the distribution of Harsanyi dividends

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