Values for rooted-tree and sink-tree digraph games and sharing a river

Khmelnitskaya, Anna Borisovna

doi:10.1007/s11238-009-9141-7

Cited by 50 publications

(51 citation statements)

References 7 publications

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“…In fact, it is straightforward to verify that also in this case it is the unique solution that satisfies the core lower bounds and the Ambec-Sprumont aspiration level upper bounds. The downstream incremental solution for river games with multiple springs was also proposed in Khmelnitskaya (2009) as the unique solution satisfying component efficiency and another property, called successor equivalence, which generalizes the so-called upper equivalence property introduced in van den Brink, van der Laan and Vasil'ev (2007) for line-graph games.…”

Section: Average Hierarchical Solutionmentioning

confidence: 99%

Fair Agreements for Sharing International Rivers with Multiple Springs and Externalities

Brink

Laan

Moes

2010

AIP Conference Proceedings

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In this paper we consider the problem of sharing water from a river among a group of agents (countries, cities, firms) located along the river. The benefit of each agent depends on the amount of water consumed by the agent. An allocation of the water among the agents is efficient when it maximizes the total benefits. To sustain an efficient water allocation, the agents can compensate each other by paying monetary transfers. Every water allocation and transfer schedule yields a welfare distribution, where the utility of an agent is equal to its benefit from the water consumption plus its monetary transfer (which can be negative). The problem of finding a fair welfare distribution can be modelled by a cooperative game.For a river with one spring and increasing benefit functions, Ambec and Sprumont (2002) propose the downstream incremental solution as the unique welfare distribution that is core-stable and satisfies the condition that no agent gets a utility payoff above its aspiration level. Ambec and Ehlers (2008) generalized the Ambec and Sprumont river game to river situations with satiable agents, i.e., the benefit function is decreasing beyond some satiation point. In such situations externalities appear, yielding a cooperative game in partition function form. In this paper we consider river situations with satiable agents and with multiple springs. For this type of river systems we propose the class of so-called weighted hierarchical solutions as the class of solutions satisfying several principles to be taken into account for solving water disputes. When every agent has an increasing benefit function (no externalities) then every weighted hierarchical solution is core-stable. In case of satiation points, it appears that every weighted hierarchical solution is independent of the externalities.

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Section: Average Hierarchical Solutionmentioning

confidence: 99%

Fair Agreements for Sharing International Rivers with Multiple Springs and Externalities

Brink

Laan

Moes

2010

AIP Conference Proceedings

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“…In line with the above description of studying fairness in the context of social welfare, recent axiomatic studies (cf. Ambec and Sprumont, 2002;Ambec and Ehlers, 2008b;Khmelnitskaya, 2010;Van den Brink et al, 2012;Béal et al, 2012) model river sharing as a cooperative game, where the axioms are imposed on the distribution of welfare to the agents. Recently, Van den Brink et al (2014) argued that, instead, the axioms should be imposed directly on the allocation of welfare derived from water use, which allows a closer link between the axioms and actual water allocation.…”

Section: Fairnessmentioning

confidence: 99%

The Economics of Transboundary River Management

Ansink

Houba

2014

SSRN Journal

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“…[20] for linegraph communication situations and by Khmelnitskaya [11] for forest-graph communication situations. Both articles also study economic applications.…”

Section: Communication Situationsmentioning

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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Values for rooted-tree and sink-tree digraph games and sharing a river

Abstract: TU game, Cooperation structure, Myerson value, Component efficiency, Deletion link property, Harsanyi dividends, Sharing a river,

Cited by 50 publications

References 7 publications

Fair Agreements for Sharing International Rivers with Multiple Springs and Externalities

Fair Agreements for Sharing International Rivers with Multiple Springs and Externalities

The Economics of Transboundary River Management

Average tree solutions and the distribution of Harsanyi dividends

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