# Sharing Non-anonymous Costs of Multiple Resources Optimally

@inproceedings{Klimm2014SharingNC, title={Sharing Non-anonymous Costs of Multiple Resources Optimally}, author={Max Klimm and Daniel Schmand}, booktitle={International/Italian Conference on Algorithms and Complexity}, year={2014} }

In cost sharing games, the existence and efficiency of pure Nash equilibria fundamentally depends on the method that is used to share the resources' costs. We consider a general class of resource allocation problems in which a set of resources is used by a heterogeneous set of selfish users. The cost of a resource is a non-decreasing function of the set of its users. Under the assumption that the costs of the resources are shared by uniform cost sharing protocols, i.e., protocols that use only…

## 17 Citations

### Existence and Efficiency of Equilibria for Cost-Sharing in Generalized Weighted Congestion Games

- EconomicsACM Trans. Economics and Comput.
- 2020

This work studies the impact of cost-sharing methods on the existence and efficiency of (pure) Nash equilibria in weighted congestion games, and proves an upper bound for the Shapley value cost- sharing method, which holds for general sets of cost functions and which is tight in special cases of interest, such as bounded degree polynomials.

### Designing Cost-Sharing Methods for Bayesian Games

- Computer Science, EconomicsTheory of Computing Systems
- 2017

This work shows an interesting connection between algorithms for Oblivious Stochastic optimization problems and cost-sharing design with low PoA, and enforces approximate solutions of the stochastic problem, as Bayesian Nash equilibria, with the same guarantees on the PoA.

### Tight Bounds for Cost-Sharing in Weighted Congestion Games

- Economics, MathematicsICALP
- 2015

The price of stability is studied and an upper bound for the Shapley value cost-sharing method is proved, which holds for general sets of cost functions and which is tight in special cases of interest, such as bounded degree polynomials.

### Cost-Sharing in Generalized Selfish Routing

- Economics
- 2017

We study a generalization of atomic selfish routing games where each player may control multiple flows which she routes seeking to minimize their aggregate cost. Such games emerge in various…

### Cost-Sharing Games in Real-Time Scheduling Systems

- Computer Science, EconomicsWINE
- 2018

This work focuses on monomial cost functions in real-time scheduling systems where the server’s activation cost in every time slot is a function of its load, and shows that the price of anarchy grows to infinity as a polynomial of the number of jobs in the game.

### Cost-Sharing in Generalised Selfish Routing

- EconomicsCIAC
- 2017

This work studies a generalisation of atomic selfish routing games where each player may control multiple flows which she routes seeking to minimise their aggregate cost and proves that the Shapley value is the only cost-sharing method that guarantees it.

### On the Price of Anarchy of Cost-Sharing in Real-Time Scheduling Systems

- Mathematics, Computer ScienceWINE
- 2019

We study cost-sharing games in real-time scheduling systems where the activation cost of the server at any given time is a function of its load. We focus on monomial cost functions and consider both…

### Quantifying Inefficiency of Fair Cost-Sharing Mechanisms for Sharing Economy

- Computer ScienceIEEE Transactions on Control of Network Systems
- 2018

The inefficiency of distributed decision-making processes under a cost-sharing mechanism by the strong price of anarchy is quantified, showing that the SPoA for equal-split, proportional- split, and usage-based cost sharing (under certain conditions) is only moderate inefficiency.

### Computing Approximate Pure Nash Equilibria in Shapley Value Weighted Congestion Games

- Economics, Computer ScienceWINE
- 2017

This work presents a novel relation that approximates the Shapley value of a player by her proportional share and vice versa and significantly improves the best known factor for computing approximate pure Nash equilibria in weighted congestion games of [7].

### Approximate Pure Nash Equilibria in Congestion, Opinion Formation and Facility Location Games

- Economics
- 2019

This thesis investigates approximate pure Nash equilibria in different game-theoretic models and bound the approximation guarantees for natural states nearly independent of the specific definition of the players' neighborhoods by applying a concept of virtual costs.

## References

SHOWING 1-10 OF 20 REFERENCES

### Optimal Cost Sharing for Resource Selection Games

- Economics, Computer ScienceMath. 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.

### Network Cost-Sharing without Anonymity

- EconomicsTEAC
- 2016

These primary results are tight bounds on the cost of strong Nash equilibria and potential function minimizers in network cost-sharing games with nonanonymous cost functions, parameterized by the set C of allowable submodular cost functions.

### Potential games are necessary to ensure pure nash equilibria in cost sharing games

- EconomicsEC '13
- 2013

This work proves that a distribution rule guarantees equilibrium existence for all games if and only if it is equivalent to a generalized weighted Shapley value on some `ground' welfare functions $W$, which can be distinct from W.

### Designing Network Protocols for Good Equilibria

- Computer ScienceSIAM J. Comput.
- 2010

This work uses a precise characterization of the cost-sharing protocols that induce only network games with pure-strategy Nash equilibria to prove, among other results, that the Shapley protocol is optimal in directed graphs and that simple priority protocols are essentially optimal in undirected graphs.

### The price of stability for network design with fair cost allocation

- Economics45th Annual IEEE Symposium on Foundations of Computer Science
- 2004

It is established that the fair cost allocation protocol is in fact a useful mechanism for inducing strategic behavior to form near-optimal equilibria, and its results are extended to cases in which users are seeking to balance network design costs with latencies in the constructed network.

### Restoring Pure Equilibria to Weighted Congestion Games

- EconomicsICALP
- 2011

This work proposes a new way of assigning costs to players with weights in congestion games that recovers the important properties of the unweighted model, and proves tight bounds on the worst-case inefficiency of equilibria.

### Atomic Resource Sharing in Noncooperative Networks

- Computer ScienceProceedings of INFOCOM '97
- 1997

It is shown that, for a class of throughput-oriented cost functions, existence of and convergence to a Nash equilibrium is guaranteed in all topologies.

### Sink equilibria and convergence

- Economics46th Annual IEEE Symposium on Foundations of Computer Science (FOCS'05)
- 2005

It is argued that there is a natural convergence process to sink equilibria in games where agents use pure strategies, and the price of sinking is an alternative measure of the social cost of a lack of coordination, which measures the worst case ratio between thevalue of a sink equilibrium and the value of the socially optimal solution.

### On the performance of user equilibria in traffic networks

- Economics, Computer ScienceSODA '03
- 2003

The performance guarantee of user equilibria when compared to constrained system optima, which are designed to be more fair, are analyzed, and improved bounds in this setting are established.