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

Abstract

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.

Uncertainty in Multi-Commodity Routing Networks: When does it help?

“…Finally, our work is thematically similar to the recent paper on the informational Braess paradox [19] whose model can be viewed as an extreme case of our model where the uncertainty parameter r θ is so high on some edges (r θ → ∞) that users always avoid such edges. On the other hand, our model is more continuous as user attitudes are parameterized by a finite value of r θ , which allows for a more realistic depiction of the tradeoffs faced by users who must balance travel time, congestion, and uncertainty.…”

“…On the other hand, our model is more continuous as user attitudes are parameterized by a finite value of r θ , which allows for a more realistic depiction of the tradeoffs faced by users who must balance travel time, congestion, and uncertainty. Although both the characterizations make use of the serially linearly independent topology, it is worth pointing out that our results do not follow from [19] and require different techniques that capture a more continuous trade-off between uncertainty and social cost.…”

“…Definition 5: (Serially Linearly Independent (SLI)) An undirected graph G with a single source s and destination t is said to belong to the serially linearly independent class if (i) G is linearly independent or (ii) G consists of two linearly independent graphs connected in serial. This extended topology was first introduced in [19]. These three topologies are related as: 1) Every linearly independent graph belongs to the serially linearly independent class.…”

Reconciling Selfish Routing with Social Good

“…However, as new technologies play a crucial role in shifting in user behavior, various incomplete information models have been introduced. Acemoglu et al [24] has discussed an informational Nash equilibrium where users converge to an equilibrium with partial knowledge of the network structure. In a related setup where each user's information is limited to a common prior on the latency functions, Vasserman et al [25] considered a mediated Bayesian Nash equilibrium (BNE).…”

Utilizing Information Optimally to Influence Distributed Network Routing

“…This inefficiency resulting from selfish behavior is commonly characterized by the ratio between the worst-case social welfare resulting from choices of self-interested users and the optimal social welfare; this is typically referred to as the price of anarchy [1] and has become a highly studied area in resource allocation [2], [3], distributed control [4], and transportation [5], [6]. A common line of research studies how this inefficiency can be mitigated by using pricing mechanisms and information systems which incentivize users to make decisions more in line with the social optimum [7], [8]. Naturally, an effective implementation of incentives is heavily dependent on how the users respond to the incentives.…”