Exact and approximate equilibria for optimal group network formation

Anshelevich, Elliot; Caskurlu, Bugra

doi:10.1016/j.tcs.2011.05.049

Cited by 15 publications

(16 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In particular, in Section 4 we explore equivalence without relying on linear programming. While in some cases like Terminal Backup Games [4] we can resort to combinatorial arguments, in other interesting games our results are mostly negative. In particular, we show that in Steiner Tree connection games or network cutting games equivalence does not hold, i.e., the core might be non-empty but a SE is absent.…”

Section: Introductionmentioning

confidence: 70%

“…In contrast, such a model is unsuitable when there is very little control over players and their bargaining options. A model that allows for general cost sharing between players is sometimes referred to as arbitrary cost sharing, and it has been studied in [4,5,7,12,15,[23][24][25][26]. In these cost sharing games the strategy of a player is a payment function that specifies his exact contribution to the cost of each resource.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Strategic cooperation in cost sharing games

Hoefer

2011

Int J Game Theory

View full text Add to dashboard Cite

In this paper we consider strategic cost sharing games with so-called arbitrary sharing based on various combinatorial optimization problems, such as vertex and set cover, facility location, and network design problems. We concentrate on the existence and computational complexity of strong equilibria, in which no coalition can improve the cost of each of its members.Our main result reveals a connection between strong equilibrium in strategic games and the core in traditional coalitional cost sharing games studied in economics. For set cover and facility location games this results in a tight characterization of the existence of strong equilibrium using the integrality gap of suitable linear programming formulations. Furthermore, it allows to derive all existing results for strong equilibria in network design cost sharing games with arbitrary sharing via a unified approach. In addition, we are able to show that in general the strong price of anarchy is always 1. This should be contrasted with the price of anarchy of Θ(n) for Nash equilibria. Finally, we indicate that the LP-approach can also be used to compute near-optimal and near-stable approximate strong equilibria.

show abstract

Section: Introductionmentioning

confidence: 70%

Section: Introductionmentioning

confidence: 99%

Strategic cooperation in cost sharing games

Hoefer

2011

Int J Game Theory

View full text Add to dashboard Cite

show abstract

“…By our choice of the two edges, we know that c (u, v (u, v, w), with the last inequality being true because of the Simplex Condition. As desired, this tells us that cost(C) ≤ cost(C * ) ≤ 4 3 cost(M * ). This approximation algorithm works since the Terminal Backup problem required only that every terminal be connected to at least one other, and so is essentially a covering problem, instead of a matching problem.…”

Section: Running Timementioning

confidence: 83%

“…In addition, all of the above variations are NP-hard, while Terminal Backup is solvable in polynomial time for k = 2. For k > 2 it becomes NP-hard, although there is a 2-approximation algorithm shown in [4] using techniques from [18].…”

Section: Related Workmentioning

confidence: 99%

See 1 more Smart Citation

Terminal Backup, 3D Matching, and Covering Cubic Graphs

Anshelevich¹,

Karagiozova²

2011

SIAM J. Comput.

Self Cite

View full text Add to dashboard Cite

Abstract. We define a problem called Simplex Matching and show that it is solvable in polynomial time. While Simplex Matching is interesting in its own right as a nontrivial extension of nonbipartite min-cost matching, its main value lies in many (seemingly very different) problems that can be solved using our algorithm. For example, suppose that we are given a graph with terminal nodes, nonterminal nodes, and edge costs. Then, the Terminal Backup problem, which consists of finding the cheapest forest connecting every terminal to at least one other terminal, is reducible to Simplex Matching. Simplex Matching is also useful for various tasks that involve forming groups of at least two members, such as project assignment and variants of facility location. In an instance of Simplex Matching, we are given a hypergraph H with edge costs and edge size at most 3. We show how to find the min-cost perfect matching of H efficiently if the edge costs obey a simple and realistic inequality that we call the Simplex Condition. The algorithm we provide is relatively simple to understand and implement but difficult to prove correct. In the process of this proof we show some powerful new results about covering cubic graphs with simple combinatorial objects.

show abstract