Abstract We consider a network pricing game on a parallel network with congestion effects in which link owners set tolls for travel so as to maximize profit. A central authority is able to regulate this competition by means of a (uniform) price cap. The first question we want to answer is how such a cap should be designed in order to minimize the total congestion. We provide an algorithm that finds an optimal price cap for networks with affine latency functions and a full support Wardrop equilibrium. Second, we consider the induced network performance at an optimal price cap. We show that for two link networks with affine latency functions, the congestion costs at the optimal price cap are at most 8 7 times the optimal congestion costs. For more general latency functions, this bound goes up to 2 under the assumption that an uncapped Nash equilibrium exists. However, in general such an equilibrium need not exist and this can be used to show that optimal price caps can induce arbitrarily inefficient flows.
@cite_18: We study the efficiency implications of competition among profit-maximizing service providers in communication networks. Service providers set prices for transmission of flows through their (sub)network. The central question is whether the presence of prices will help or hinder network performance. We investigate this question by considering the difference between users' willingness to pay and delay costs as the efficiency metric. Previous work has demonstrated that in networks consisting of parallel links, efficiency losses from competition are bounded. Nevertheless, parallel-link networks are special, and in most networks, traffic has to simultaneously traverse links (or subnetworks) operated by independent service providers. The simplest network topology allowing this feature is the parallel-serial structure, which we study in this paper. In contrast to existing results, we show that in the presence of serial links, the efficiency loss relative to the social optimum can be arbitrarily large. The reason for this degradation of performance is the double marginalization problem, whereby each serial provider charges high prices not taking into account the effect of this strategy on the profits of other providers along the same path. Nevertheless, when there are no delay costs without transmission (i.e., latencies at zero are equal to zero), irrespective of the number of serial and parallel providers, the efficiency of strong oligopoly equilibria can be bounded by 1 2, where strong oligopoly equilibria are equilibria in which each provider plays a strict best response and all of the traffic is transmitted. However, even with strong oligopoly equilibria, inefficiency can be arbitrarily large when the assumption of no delay costs without transmission is relaxed.
@cite_47: The success of the Internet is remarkable in light of the decentralized manner in which it is designed and operated. Unlike small scale networks, the Internet is built and controlled by a large number of disparate service providers who are not interested in any global optimization. Instead, providers simply seek to maximize their own profit by charging users for access to their service. Users themselves also behave selfishly, optimizing over price and quality of service. Game theory provides a natural framework for the study of such a situation. However, recent work in this area tends to focus on either the service providers or the network users, but not both. This paper introduces a new model for exploring the interaction of these two elements, in which network managers compete for users via prices and the quality of service provided. We study the extent to which competition between service providers hurts the overall social utility of the system.
@cite_42: In this paper, we present a combined study of price competition and traffic control in a congested network. We study a model in which service providers own the routes in a network and set prices to maximize their profits, while users choose the amount of flow to send and the routing of the flow according to Wardrop's principle. When utility functions of users are concave and have concave first derivatives, we characterize a tight bound of 2-3 on efficiency in pure strategy equilibria of the price competition game. We obtain the same bound under the assumption that there is no fixed latency cost, i.e., the latency of a link at zero flow is equal to zero. These bounds are tight even when the numbers of routes and service providers are arbitrarily large. © 2008 Wiley Periodicals, Inc. NETWORKS, 2008
@cite_8: We study the efficiency of oligopoly equilibria (OE) in congested markets. The motivating examples are the allocation of network flows in a communication network or of traffic in a transportation network. We show that increasing competition among oligopolists can reduce efficiency, measured as the difference between users' willingness to pay and delay costs. We characterize a tight bound of 5 6 on efficiency in pure strategy equilibria when there is zero latency at zero flow and a tight bound of 2√2 - 2 with positive latency at zero flow. These bounds are tight even when the numbers of routes and oligopolists are arbitrarily large.
Acemoglu and Ozdaglar @cite_8 introduce a model of price competition between link owners in a parallel network that is very similar to ours. The main difference is that in their model users have a reservation value for travel. This implies that if links become too expensive users choose not to travel, whereas in our model users always travel through the network. Their main result is a (tight) bound on the inefficiency of equilibria. Later several generalizations of the model were introduced. The follow-up work of Acemoglu and Ozdaglar @cite_18 allow for a slightly more general topology, namely parallel paths with multiple links, and show that equilibria can be arbitrarily inefficient. @cite_47 consider the model with elastic traffic demand. Their bounds on inefficiency, however, are not tight, which is improved upon by Ozdaglar @cite_42 .