The complexity of welfare maximization in congestion games

Meyers, Carol; Schulz, Andreas S.

doi:10.1002/net.20439

Cited by 28 publications

(26 citation statements)

References 24 publications

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“…, N . This follows from the NPhardness of asymmetric N [14]. The next two theorems show that finding socially optimal states in the combinatorial games that we have introduced is NP-hard.…”

Section: Np-hardnessmentioning

confidence: 79%

See 1 more Smart Citation

Totally Unimodular Congestion Games

Pia¹,

Ferris²,

Michini³

2017

Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms

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We investigate a new class of congestion games, called Totally Unimodular (TU) Congestion Games, where the players' strategies are binary vectors inside polyhedra defined by totally unimodular constraint matrices. Network congestion games belong to this class.In the symmetric case, when all players have the same strategy set, we design an algorithm that finds an optimal aggregated strategy and then decomposes it into the single players' strategies. This approach yields strongly polynomial-time algorithms to (i) find a pure Nash equilibrium, and (ii) compute a socially optimal state, if the delay functions are weakly convex. We also show how this technique can be extended to matroid congestion games.We then introduce some combinatorial TU congestion games, where the players' strategies are matchings, vertex covers, edge covers, and stable sets of a given bipartite graph. In the asymmetric case, we show that for these games (i) it is PLS-complete to find a pure Nash equilibrium even in case of linear delay functions, and (ii) it is NP-hard to compute a socially optimal state, even in case of weakly convex delay functions.

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“…, N . This follows from the NPhardness of asymmetric N [14]. The next two theorems show that finding socially optimal states in the combinatorial games that we have introduced is NP-hard.…”

Section: Np-hardnessmentioning

confidence: 79%

“…We remark that the weak convexity assumption in Theorem 3.2 is necessary, since for general nondecreasing delay functions computing a socially optimal state of a symmetric TU congestion game is NP-hard [14].…”

Section: Socially Optimal Statesmentioning

confidence: 99%

Totally Unimodular Congestion Games

Pia¹,

Ferris²,

Michini³

2017

Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms

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“…Meyers and Schulz [17] classified the complexity of computing a social optimum for general congestion games as well as network congestion games and differentiated between asymmetric and symmetric strategy spaces. In the case of network congestion games, they also distinguished the case in which all players share a common source.…”

Section: Literature Reviewmentioning

confidence: 99%

A logarithmic approximation for polymatroid congestion games

Harks

Oosterwijk

Vredeveld

2016

Operations Research Letters

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We study the problem of computing a social optimum (minimum cost solution) in polymatroid congestion games, where the strategy space of every player consists of the set of vectors in a playerspecific integral polymatroid base polyhedron defined on the ground set of resources. For general non-decreasing cost functions we devise an H rk -approximation algorithm, where rk is the sum of the ranks of the player-specific polymatroids and H rk denotes the rk-th harmonic number. The main idea of our algorithm is to iteratively increase resource utilization in a greedy fashion and to invoke a polynomial covering oracle that checks feasibility of every computed resource utilization. The approximation guarantee is best possible up to a constant factor. As a special case, our result 2) where the complexity of computing a socially optimal solution for matroid congestion games with non-decreasing cost functions is considered. Here, the approximation guarantee is best possible up to a constant factor if the number of resources is polynomially bounded in the number of players.

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“…Our work also relates to a large body of work in the game theory literature on finding social optimally solutions, such as work on maximizing welfare in congestion games [19,20], auctions [21,22] and social choices [23]. However, to the best of our knowledge, there has been no work on learning socially optimal rankings from noisy user feedback.…”

Section: Related Workmentioning

confidence: 99%

Learning Socially Optimal Information Systems from Egoistic Users

Raman

Joachims

2013

Advanced Information Systems Engineering

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Abstract. Many information systems aim to present results that maximize the collective satisfaction of the user population. The product search of an online store, for example, needs to present an appropriately diverse set of products to best satisfy the different tastes and needs of its user population. To address this problem, we propose two algorithms that can exploit observable user actions (e.g. clicks) to learn how to compose diverse sets (and rankings) that optimize expected utility over a distribution of utility functions. A key challenge is that individual users evaluate and act according to their own utility function, but that the system aims to optimize collective satisfaction. We characterize the behavior of our algorithms by providing upper bounds on the social regret for a class of submodular utility functions in the coactive learning model. Furthermore, we empirically demonstrate the efficacy and robustness of the proposed algorithms for the problem of search result diversification.

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The complexity of welfare maximization in congestion games

Cited by 28 publications

References 24 publications

Totally Unimodular Congestion Games

Totally Unimodular Congestion Games

A logarithmic approximation for polymatroid congestion games

Learning Socially Optimal Information Systems from Egoistic Users

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