On Multidimensional Congestion Games

Bilò, Vittorio; Flammini, Michele; Gallotti, Vasco; Vinci, Cosimo

doi:10.3390/a13100261

Cited by 5 publications

(3 citation statements)

References 36 publications

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“…It would be interesting to see, whether one can achieve similar results for variants and generalizations of congestion games such as weighted [3], atomic-or integersplittable [27,32] congestion games, scheduling games [16,17,20], etc. Considering other heuristics such as greedy or one-round walks [5,7,15,21] would be another natural direction.…”

Section: Conclusion and Open Problemsmentioning

confidence: 99%

Improving Approximate Pure Nash Equilibria in Congestion Games

Vijayalakshmi

Skopalik

2020

Web and Internet Economics

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Congestion games constitute an important class of games to model resource allocation by different users. As computing an exact [18] or even an approximate [34] pure Nash equilibrium is in general PLScomplete, Caragiannis et al. [9] present a polynomial-time algorithm that computes a (2 + )-approximate pure Nash equilibria for games with linear cost functions and further results for polynomial cost functions. We show that this factor can be improved to (1.61 + ) and further improved results for polynomial cost functions, by a seemingly simple modification to their algorithm by allowing for the cost functions used during the best response dynamics be different from the overall objective function. Interestingly, our modification to the algorithm also extends to efficiently computing improved approximate pure Nash equilibria in games with arbitrary non-decreasing resource cost functions. Additionally, our analysis exhibits an interesting method to optimally compute universal load dependent taxes and using linear programming duality prove tight bounds on the PoA under universal taxation, e.g., 2.012 for linear congestion games and further results for polynomial cost functions. Although our approach yield weaker results than that in Bilò and Vinci [6], we remark that our cost functions are locally computable and in contrast to [6] are independent of the actual instance of the game. Keywords: Congestion games • Approximate pure Nash equilibria • Price of anarchy • Universal taxes V. R. Vijayalakshmi-This work is supported by the German research council (DFG) Research Training Group 2236 UnRAVeL

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Section: Conclusion and Open Problemsmentioning

confidence: 99%

Improving Approximate Pure Nash Equilibria in Congestion Games

Vijayalakshmi

Skopalik

2020

Web and Internet Economics

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“…The upper bounds on the price of anarchy are established through the primal-dual method (Bilò 2018;Bilò and Vinci 2023). This method relies on a pair of primal-dual formulations and, in particular, exploits the fact that, usually, the dual program possesses a very simple structure.…”

Section: Our Contributionmentioning

confidence: 99%

“…To obtain the upper bounds, we resort to the primal-dual method developed in (Bilò 2018;Bilò and Vinci 2023). Before presenting our main result, we need the following technical lemma.…”

Section: Price Of Anarchymentioning

confidence: 99%

Enhancing the Efficiency of Altruism and Taxes in Affine Congestion Games through Signalling

Bilò,

Vinci

2024

AAAI

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We address the problem of improving the worst-case efficiency of pure Nash equilibria (aka, the price of anarchy) in affine congestion games, through a novel use of signalling. We assume that, for each player in the game, a most preferred strategy is publicly signalled. This can be done either distributedly by the players themselves, or be the outcome of some centralized algorithm. We apply this signalling scheme to two well-studied scenarios: games with partially altruistic players and games with resource taxation. We show a significant improvement in the price of anarchy of these games, whenever the aggregate signalled strategy profile is a good approximation of the game social optimum.

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Nash Social Welfare in Selfish and Online Load Balancing

Bilò

Monaco

Moscardelli

et al. 2022

ACM Trans. Econ. Comput.

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In load balancing problems there is a set of clients, each wishing to select a resource from a set of permissible ones, in order to execute a certain task. Each resource has a latency function, which depends on its workload, and a client’s cost is the completion time of her chosen resource. Two fundamental variants of load balancing problems are selfish load balancing (aka. load balancing games ), where clients are non-cooperative selfish players aimed at minimizing their own cost solely, and online load balancing , where clients appear online and have to be irrevocably assigned to a resource without any knowledge about future requests. We revisit both problems under the objective of minimizing the Nash Social Welfare , i.e., the geometric mean of the clients’ costs. To the best of our knowledge, despite being a celebrated welfare estimator in many social contexts, the Nash Social Welfare has not been considered so far as a benchmarking quality measure in load balancing problems. We provide tight bounds on the price of anarchy of pure Nash equilibria and on the competitive ratio of the greedy algorithm under very general latency functions, including polynomial ones. For this particular class, we also prove that the greedy strategy is optimal, as it matches the performance of any possible online algorithm.

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On Multidimensional Congestion Games

Cited by 5 publications

References 36 publications

Improving Approximate Pure Nash Equilibria in Congestion Games

Improving Approximate Pure Nash Equilibria in Congestion Games

Enhancing the Efficiency of Altruism and Taxes in Affine Congestion Games through Signalling

Nash Social Welfare in Selfish and Online Load Balancing

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