@article{Harks2014ResourceBG,
author={Tobias Harks and Britta Peis},
journal={Algorithmica},
year={2014},
volume={70},
pages={493-512}
}
• Published 18 April 2012
• Economics
• Algorithmica
In resource buying games a set of players jointly buys a subset of a finite resource set $$E$$E (e.g., machines, edges, or nodes in a digraph). The cost of a resource $$e$$e depends on the number (or load) of players using $$e$$e, and has to be paid completely by the players before it becomes available. Each player $$i$$i needs at least one set of a predefined family $${\mathcal S}_i\subseteq 2^E$$Si⊆2E to be available. Thus, resource buying games can be seen as a variant of congestion games in…
11 Citations
Efficient Black-Box Reductions for Separable Cost Sharing
• Economics
ICALP
• 2018
In cost sharing games with delays, a set of agents jointly allocates a finite subset of resources and a separable protocol determines cost shares that satisfy budget balance on every resource and separability over the resources.
Efficiency of Equilibria in Uniform Matroid Congestion Games
• Mathematics, Economics
SAGT
• 2016
This paper considers congestion games with affine cost functions where the strategy spaces of players are symmetric and equal to the set of bases of a k-uniform matroid, and shows that the price of anarchy is strictly larger than theprice of anarchy for singleton strategy spaces where the latter is 4/3.
Generalizations of Weighted Matroid Congestion Games: Pure Nash Equilibrium, Sensitivity Analysis, and Discrete Convex Function
This paper proves the existence of pure Nash equilibria in matroid congestion games with monotone cost functions, and conducts sensitivity analysis for separable convex optimization over base polyhedra by Harks, Klimm, and Peis (2018).
Quality of equilibria in resource allocation games
In situations where multiple parties are involved, local or selfish decisions result in outcomes that rarely align with what is best for society. In order to evaluate the quality of the resulting
Near-Optimality in Covering Games by Exposing Global Information
• Economics
TEAC
• 2014
The first results that carefully constructed advice vectors yield stronger guarantees are given, showing how to efficiently construct an advice vector with a particular structure with cost O(log n) times the optimal social cost, and it is proved that the system quickly converges to an equilibrium with social cost of this same order.
LP-Based Covering Games with Low Price of Anarchy
• Mathematics, Economics
Theory of Computing Systems
• 2014
We design a new class of vertex and set cover games, where the price of anarchy bounds match the best known constant factor approximation guarantees for the centralized optimization problems for
Uniqueness of equilibria in atomic splittable polymatroid congestion games
• Economics
ISCO
• 2016
It is shown that important cases such as base orderable matroids can be recovered as a special case of bidirectional flow polymatroids, and matroidal set systems are in some sense necessary to guarantee uniqueness of equilibria.
A Characterization of Undirected Graphs Admitting Optimal Cost Shares
• Mathematics
WINE
• 2017
One of the most intriguing open problems to date is to understand the power of budget-balanced and separable cost sharing protocols in order to induce low-cost Steiner forests.
Matroids Are Immune to Braess' Paradox
• Mathematics
Math. Oper. Res.
• 2017
This paper considers general nonatomic congestion games and gives a characterization of the maximal combinatorial property of strategy spaces for which Braess paradox does not occur, and proves its characterization by two novel sensitivity results for convex separable optimization problems over polymatroid base polyhedra.

## References

SHOWING 1-10 OF 21 REFERENCES
Competitive Cost Sharing with Economies of Scale
This work considers a general class of non-cooperative buy-at-bulk cost sharing games, in which k players make investments to purchase a set of resources, and considers the existence and total cost of pure-strategy exact and approximate Nash equilibria.
Optimal Cost Sharing for Resource Selection Games
• Economics, Computer Science
Math. Oper. Res.
• 2013
This work studies cost sharing in resource selection games where the strategy spaces are either singletons or bases of a matroid defined on the ground set of resources and finds optimal basic and separable protocols that guarantee the price of stability and price of anarchy to grow logarithmically in the number of players.
On the Complexity of Pure-Strategy Nash Equilibria in Congestion and Local-Effect Games
• Economics
Math. Oper. Res.
• 2008
It is proved that it actually is strongly NP-hard to determine whether a given weighted network congestion game has a pure-strategy Nash equilibrium, regardless of whether flow is unsplittable (has to be routed on a single path for each player) or not.
Non-Cooperative Tree Creation
This paper proposes polynomial time algorithms for computing approximate Nash equilibria, which provide relaxed stability and cost efficiency guarantees for tree connection games and uses a novel iteration technique for trees that might be of independent interest.
Near-optimal network design with selfish agents
• Economics, Computer Science
STOC '03
• 2003
This paper proves that there is a Nash equilibrium as cheap as the optimal network, and gives a polynomial time algorithm to find a (1+ε)-approximate Nash equilibrium that does not cost much more.
Strategic cooperation in cost sharing games
• M. Hoefer
• Computer Science
Int. J. Game Theory
• 2010
The main result reveals a connection to the core in coalitional cost sharing games studied in operations research and indicates how the LP-approach is useful for the computation of near-optimal and near-stable approximate strong equilibria (SE).
On the Impact of Combinatorial Structure on Congestion Games
• Economics
2006 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS'06)
• 2006
An approach is presented that enables us to devise hardness proofs for various kinds of combinatorial games, including first results about the hardness of market sharing games and congestion games for overlay network design.
Price of Stability in Survivable Network Design
• Economics, Computer Science
Theory of Computing Systems
• 2011
It is shown that there always exists a 2-approximate Nash equilibrium that is as good as the centralized optimum and price of stability is 1 for the general version of the Survivable Connection Game.