A monotonic and merge-proof rule in minimum cost spanning tree situations

Gómez-Rúa, María; Vidal-Puga, Juan

doi:10.1007/s00199-016-0996-x

Cited by 9 publications

(3 citation statements)

References 44 publications

(40 reference statements)

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“…The second selects the agents iteratively and the total connection cost in each iteration is shared equally among the agents selected in this iteration. We also show that these mechanisms satisfy other desirable properties studied in the literature [4,8,13,20,26].…”

Section: Introductionsupporting

confidence: 68%

Cost Sharing under Private Valuation and Connection Control

Zhang¹,

Zhang²,

Gu³

et al. 2023

Preprint

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We consider a cost sharing problem on a weighted undirected graph, where all the nodes want to connect to a special node called source, and they need to share the total cost (weights) of the used edges. Each node except for the source has a private valuation of the connection, and it may block others' connections by strategically cutting its adjacent edges to reduce its cost share, which may increase the total cost. We aim to design mechanisms to prevent the nodes from misreporting their valuations and cutting their adjacent edges. We first show that it is impossible for such a mechanism to further satisfy budget balance (cover the total cost) and efficiency (maximize social welfare). Then, we design two feasible cost sharing mechanisms that incentivize each node to offer all its adjacent edges and truthfully report its valuation, and also satisfy either budget balance or efficiency.

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Section: Introductionsupporting

confidence: 68%

Cost Sharing under Private Valuation and Connection Control

Zhang¹,

Zhang²,

Gu³

et al. 2023

Preprint

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“…See also the literature on the airport problem ( [20]) and the more general minimal cost spanning tree problem (mcst) (e.g., [3], [10], [6]). There as here participants in the division process are entirely described by objective parameters (legally valid claims in the bankruptcy problem; veri…able stand-alone costs in the airport problem; veri…able connection costs in the mcst problem) with no relation to standard microeconomic characteristics like preferences, risk aversion, etc..…”

Section: Relation To the Literaturementioning

confidence: 99%

“…The Ex-ante and Ex-post rules select approximately the same cost shares. 6 However if we learn that b is much more expensive than a, it makes sense to charge signi…cantly more to Ann (as the Needs Priority rule will do) because she is more liable for b than Chris, and most of the costs come from b.…”

Section: Three Separability Properties 41 Cost Additivitymentioning

confidence: 99%

Sharing the cost of risky projects

Hougaard

Moulin

2017

Econ Theory

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Users share the cost of unreliable non rival projects (items). For instance, industry partners pay today for R&D that may or may not deliver a cure to some viruses, agents pay for the edges of a network that will cover their connectivity needs, but the edges may fail, etc.. Each user has a binary inelastic need that is served if and only if certain subsets of items are actually functioning. We ask how should the cost be divided when individual needs are heterogenous. We impose three powerful separability properties:Independence of Timing ensures that the cost shares computed ex ante are the expectation, over the random realization of the projects, of shares computed ex post. Cost Additivity together with Separability Across Projects ensure that the cost shares of an item depend only upon the service provided by that item for a given realization of all other items.Combining these with fair bounds on the liability of agents with more or less ‡exible needs, and of agents for whom an item is either indispensable or useless, we characterize two rules: the Ex Post Service rule is the expectation of the equal division of costs between the agents who end up served; the Needs Priority rule splits the cost …rst between those agents for whom an item is critical ex post, or if there are no such agents between those who end up being served.

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