Noncooperative cost spanning tree games with budget restrictions

Bergantiños, Gustavo; Lorenzo, Leticia

doi:10.1002/nav.20319

Cited by 7 publications

(5 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Some studies treated the problem from the perspective of a non-cooperative game. Bergantiños and Lorenzo [2] studied the Nash equilibrium of the problem and further they [3] studied the Nash equilibrium with budget restriction. Tijs and Driessen [25] proposed the cost gap allocation (CGA) method, but it only applies to complete graphs.…”

Section: Related Workmentioning

confidence: 99%

Cost Sharing under Private Valuation and Connection Control

Zhang¹,

Zhang²,

Gu³

et al. 2023

Preprint

View full text Add to dashboard Cite

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.

show abstract

Section: Related Workmentioning

confidence: 99%

Cost Sharing under Private Valuation and Connection Control

Zhang¹,

Zhang²,

Gu³

et al. 2023

Preprint

View full text Add to dashboard Cite

show abstract

“…• Minimum-cost spanning tree problems with revenues (Bergantiños and Lorenzo 2008; Estévez-Fernández and Reijnierse 2014) are games where some agents have a limited budget, i.e., they connect if their assigned payment is not more than their connection revenue, or budget. These problems also generalize minimum-cost spanning tree problems where some agents are indifferent.…”

Section: Relation Between Coresmentioning

confidence: 99%

“…For instance, several towns may draw power from a common power plant, and hence have to share the cost of the distribution network (Dutta and Kar 2004). Bergantiños and Lorenzo (2004, 2005, 2008) study a real situation where villagers had to pay the cost of constructing pipes from their respective houses to a water supplier. Other examples include communication networks, such as telephone, Internet, or cable television.…”

Section: Introductionmentioning

confidence: 99%

“…Thus, agents bargain among themselves, following such bargaining protocol, how to divide the cost. Papers using this approach in mcst p are Bergantiños and Lorenzo (2004, 2005, 2008, Moulin and Velez (2013), Hernández et al (2016). Other non-cooperative results are part of a relevant research agenda known as the Nash program for cooperative games.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A review of cooperative rules and their associated algorithms for minimum-cost spanning tree problems

Cid

Puga

2021

SERIEs

Self Cite

View full text Add to dashboard Cite

Minimum-cost spanning tree problems are well-known problems in the operations research literature. Some agents, located at different geographical places, want a service provided by a common supplier. Agents will be served through costly connections. Some part of the literature has focused, mainly, in studying how to allocate the connection cost among the agents. We review the papers that have addressed the allocation problem using cooperative game theory. We also relate the rules defined through cooperative games with rules defined directly from the problem, either through algorithms for computing a minimal tree, either through a cone-wise decomposition.

show abstract

“…Thus, each rule depends on a vector of weights (w i ) i∈N in such a way that, the larger the weight of an agent is, the more the agent pays. Suppose that the source is a dam which provides water for people in a valley, as in Bergantiños and Lorenzo (2008) [2]. Since there are farmers and householders in the valley, agents achieve different benefits from water supply reliability.…”

Section: Introductionmentioning

confidence: 99%

A generalization of obligation rules for minimum cost spanning tree problems

Bergantiños

Lorenzo

Lorenzo-Freire

2011

European Journal of Operational Research

Self Cite

View full text Add to dashboard Cite

Tijs et al (2006) [23] introduce the family of obligation rules for minimum cost spanning tree problems. We give a generalization of such family. We prove that our family coincides with the set of rules satisfying an additivity property and a cost monotonicity property. We also provide two new characterizations for the family of obligation rules using the previous properties. In the first one we add a property of separability; and in the second one we add core selection.

show abstract

Noncooperative cost spanning tree games with budget restrictions

Cited by 7 publications

References 15 publications

Cost Sharing under Private Valuation and Connection Control

Cost Sharing under Private Valuation and Connection Control

A review of cooperative rules and their associated algorithms for minimum-cost spanning tree problems

A generalization of obligation rules for minimum cost spanning tree problems

Contact Info

Product

Resources

About