Network Characterizations for Excluding Braess’s Paradox

Chen, Xujin; Diao, Zhuo; Hu, Xiaodong

doi:10.1007/s00224-016-9710-4

Cited by 14 publications

(19 citation statements)

References 21 publications

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“…In concluding this subsection we should note that BP with multiple origin destination pairs has been studied in Epstein et al [2009], Lin et al [2011], Fujishige et al [2015], Holzman and Monderer [2015], and Chen et al [2016]. In particular, Chen et al [2016] provide a full characterization of network topologies for which BP occurs with multiple origin-destination pairs. BP as defined in Chen et al [2016] occurs if adding an edge (decreasing cost of an edge) increases the equilibrium (see Chen et al [2016]) while we showed IBP does not occur in this network.…”

Section: The Types Of Users Arementioning

confidence: 99%

Informational Braess’ Paradox: The Effect of Information on Traffic Congestion

Acemoğlu

Makhdoumi

Malekian

et al. 2018

Operations Research

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To systematically study the implications of additional information about routes provided to certain users (e.g., via GPS-based route guidance systems), we introduce a new class of congestion games in which users have differing information sets about the available edges and can only use routes consisting of edges in their information set. After defining the notion of Information Constrained Wardrop Equilibrium (ICWE) for this class of congestion games and studying its basic properties, we turn to our main focus: whether additional information can be harmful (in the sense of generating greater equilibrium costs/delays). We formulate this question in the form of Informational Braess' Paradox (IBP), which extends the classic Braess' Paradox in traffic equilibria, and asks whether users receiving additional information can become worse off. We provide a comprehensive answer to this question showing that in any network in the series of linearly independent (SLI) class, which is a strict subset of series-parallel networks, IBP cannot occur, and in any network that is not in the SLI class, there exists a configuration of edge-specific cost functions for which IBP will occur. In the process, we establish several properties of the SLI class of networks, which include the characterization of the complement of the SLI class in terms of embedding a specific set of networks, and also an algorithm which determines whether a graph is SLI in linear time. We further prove that the worst-case inefficiency performance of ICWE is no worse than the standard Wardrop equilibrium. * We thank anonymous referees as well as participants at several seminars and conferences for useful suggestions and comments.

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Section: The Types Of Users Arementioning

confidence: 99%

Informational Braess’ Paradox: The Effect of Information on Traffic Congestion

Acemoğlu

Makhdoumi

Malekian

et al. 2018

Operations Research

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“…cheaper Steiner forest (q 1 and tight alternative for Player 2) 3d, 3e, 4f, 4g, 5,7,8,9,11 e is completely paid For NBC12, we do not get a contradiction directly. We only get that there has to be an edge e τ in {e µ , .…”

Section: Nbc8dmentioning

confidence: 79%

“…For asymmetric (multi-commodity) games, only trees or nodes with parallel edges are efficient. These works are closely related to Milchtaichs [30] work on the Braess paradox (see also [5,8,9]). 1 Uniform protocols require that the cost shares on an edge only depend on the edge cost and the set of players, but not on the network itself.…”

Section: Related Workmentioning

confidence: 87%

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A Characterization of Undirected Graphs Admitting Optimal Cost Shares

Harks

Huber

Surek

2017

Web and Internet Economics

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In a seminal paper, Chen, Roughgarden and Valiant [7] studied cost sharing protocols for network design with the objective to implement a low-cost Steiner forest as a Nash equilibrium of an induced cost-sharing game. 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. In this work, we focus on undirected networks and analyze topological properties of the underlying graph so that an optimal Steiner forest can be implemented as a Nash equilibrium (by some separable cost sharing protocol) independent of the edge costs. We term a graph efficient if the above stated property holds. As our main result, we give a complete characterization of efficient undirected graphs for two-player network design games: an undirected graph is efficient if and only if it does not contain (at least) one out of few forbidden subgraphs. Our characterization implies that several graph classes are efficient: generalized series-parallel graphs, fan and wheel graphs and graphs with small cycles.

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“…the directed subgraph homeomorphism problem without node mapping, by providing another pattern graph for which a polynomial time algorithm exists.Contribution In this paper, we disprove this conjecture. First of all, we prove NP-hardness of checking and removing redundancy in directed multigraphs, thus formalizing the informal claim in [5]. Then, we provide a graph-theoretic characterisation of vulnerable directed nets, by proving that a directed multigraph is vulnerable if and only if it contains the graph W underlying the Wheatstone…”

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confidence: 94%

A Polynomial-Time Algorithm for Detecting the Possibility of Braess Paradox in Directed Graphs

2018

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A directed multigraph is said vulnerable if it can generate Braess paradox in Traffic Networks. In this paper, we give a graph-theoretic characterisation of vulnerable directed multigraphs; analogous results appeared in the literature only for undirected multigraphs and for a specific family of directed multigraphs. The proof of our characterisation also provides an algorithm that checks if a multigraph is vulnerable in O(|V | · |E| 2 ); this is the first polynomial time algorithm that checks vulnerability for general directed multigraphs. The resulting algorithm also contributes to another well known problem, i.e. the directed subgraph homeomorphism problem without node mapping, by providing another pattern graph for which a polynomial time algorithm exists.Contribution In this paper, we disprove this conjecture. First of all, we prove NP-hardness of checking and removing redundancy in directed multigraphs, thus formalizing the informal claim in [5]. Then, we provide a graph-theoretic characterisation of vulnerable directed nets, by proving that a directed multigraph is vulnerable if and only if it contains the graph W underlying the Wheatstone

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Network Characterizations for Excluding Braess’s Paradox

Cited by 14 publications

References 21 publications

Informational Braess’ Paradox: The Effect of Information on Traffic Congestion

Informational Braess’ Paradox: The Effect of Information on Traffic Congestion

A Characterization of Undirected Graphs Admitting Optimal Cost Shares

A Polynomial-Time Algorithm for Detecting the Possibility of Braess Paradox in Directed Graphs

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