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

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 Braes' 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

The Efficiency of Best-Response Dynamics

Best response (BR) dynamics is a natural method by which players proceed toward a pure Nash equilibrium via a local search method. The quality of the equilibrium reached may depend heavily on the order by which players are chosen to perform their best response moves. A {\em deviator rule} $S$ is a method for selecting the next deviating player. We provide a measure for quantifying the performance of different deviator rules. The {\em inefficiency} of a deviator rule $S$ is the maximum ratio, over all initial profiles $p$, between the social cost of the worst equilibrium reachable by $S$ from $p$ and the social cost of the best equilibrium reachable from $p$. This inefficiency always lies between $1$ and the {\em price of anarchy}. We study the inefficiency of various deviator rules in network formation games and job scheduling games (both are congestion games, where BR dynamics always converges to a pure NE). For some classes of games, we compute optimal deviator rules. Furthermore, we define and study a new class of deviator rules, called {\em local} deviator rules. Such rules choose the next deviator as a function of a restricted set of parameters, and satisfy a natural condition called {\em independence of irrelevant players}. We present upper bounds on the inefficiency of some local deviator rules, and also show that for some classes of games, no local deviator rule can guarantee inefficiency lower than the price of anarchy