Abstract
A common assumption in network optimization models is that a central authority controls the whole system. However, in some applications there are independent users, and assuming that they will follow directions given by an authority is not realistic. Individuals will only accept directives if they are in their own interest or if there are incentives that encourage them to do so. Actually, it would be much easier to let users make their own decisions hoping that the outcome will be close to the authority's goals. Our main contribution is to show that, in static networks subject to congestion, users' selfish decisions drive the system close to optimality with respect to various common objectives. This connection to individual decision making proves fruitful; not only does it provide us with insights and additional understanding of network problems, but it also allows us to design approximation algorithms for computationally difficult problems.
More specifically, the conflicting objectives of the users prompt the definition of a network game in which they minimize their own latencies. We show that the so-called price of anarchy is small in a quite general setting. Namely, for networks with side constraints and non-convex, non-differentiable, and even discontinuous latency functions, we show that although an arbitrary equilibrium need not be efficient, the total latency of the best equilibrium is close to that of an optimal solution. In addition, when the measure of the solution quality is the maximum latency, equilibria in networks without constraints are also near-optimal. We provide the first analysis of the problem of minimizing that objective in static networks with congestion. As this problem is NP-hard, computing an equilibrium represents a constant-factor approximation algorithm.
In some situations, the network authority might still want to do better than in equilibrium. We propose to use a solution that minimizes the total latency, subject to constraints designed to improve the solution's fairness. For several real-world instances, we compute traffic assignments of notably smaller total latency than an equilibrium, yet of similar fairness. Furthermore, we provide theoretical results that explain the conclusions derived from the computational study.