Working Paper Series 14 / 2006 Congestion pricing and non-cooperative games in communication networks (original) (raw)

Congestion Pricing and Noncooperative Games in Communication Networks

Operations Research, 2007

We consider congestion pricing as a mechanism for sharing bandwidth in communication networks, and model the interaction among the users as a game. We propose a decentralized algorithm for the users that is based on the history of the price process, where user response to congestion prices is analogous to “fictitious play” in game theory, and show that this results in convergence to the unique Wardrop equilibrium. We further show that the Wardrop equilibrium coincides with the welfare-maximizing capacity allocation.

Network resource allocation and a congestion game

PROCEEDINGS OF THE ANNUAL ALLERTON …, 2003

We explore the properties of a congestion game where users of a congested resource anticipate the effect of their actions on the price of the resource. When users are sharing a single resource, we show existence and uniqueness of the Nash equilibrium, and establish that the aggregate utility received by the users is at least 3/4 of the maximum possible aggregate utility. We also consider extensions to a network context, where users submit individual payments for each link in the network which they may wish to use. In this network model, we again show that the selfish behavior of the users leads to an aggregate utility which is no worse than 3/4 the maximum possible aggregate utility. We also show that the same analysis extends to a wide class of resource allocation systems where end users simultaneously require multiple scarce resources. These results form part of a growing literature on the "price of anarchy," i.e., the extent to which selfish behavior affects system efficiency.

Solution-based congestion games

In this paper we develop the theory of potential of cooperative games for semivalues, characterize congestion models that are defined by semivalues, and suggest an application of these results to combinatorial auctions, which may explain the success of the Iowa electronic market. and they have been analyzed by several researchers from various additional fields, in particular computer science 2 , communication networks 3 , and economics/game theory. 4

A game theoretic framework for bandwidth allocation and pricing in broadband networks

IEEE/ACM Transactions on Networking, 2000

In this paper, we present a game theoretic framework for bandwidth allocation for elastic services in high-speed networks. The framework is based on the idea of the Nash bargaining solution from cooperative game theory, which not only provides the rate settings of users that are Pareto optimal from the point of view of the whole system, but are also consistent with the fairness axioms of game theory. We first consider the centralized problem and then show that this procedure can be decentralized so that greedy optimization by users yields the system optimal bandwidth allocations. We propose a distributed algorithm for implementing the optimal and fair bandwidth allocation and provide conditions for its convergence. The paper concludes with the pricing of elastic connections based on users' bandwidth requirements and users' budget. We show that the above bargaining framework can be used to characterize a rate allocation and a pricing policy which takes into account users' budget in a fair way and such that the total network revenue is maximized.

Symmetry in Network Congestion Games: Pure Equilibria and Anarchy Cost

2005

We study computational and coordination efficiency issues of Nash equilibria in symmetric network congestion games. We first propose a simple and natural greedy method that computes a pure Nash equilibrium with respect to traffic congestion in a network. In this algorithm each user plays only once and allocates her traffic to a path selected via a shortest path computation. We then show that this algorithm works for series-parallel networks when users are identical or when users are of varying demands but have the same best response strategy for any initial network traffic. We also give constructions where the algorithm fails if either the above condition is violated (even for series-parallel networks) or the network is not series-parallel (even for identical users). Thus, we essentially indicate the limits of the applicability of this greedy approach. We also study the price of anarchy for the objective of maximum latency. We prove that for any network of m uniformly related links and for identical users, the price of anarchy is \({\it \Theta}({\frac{{\rm log} m}{{\rm log log} m}}\) ).

Optimizing the Social Cost of Congestion Games by Imposing Variable Delays

We describe a new coordination mechanism for non-atomic congestion games that leads to a (selfish) social cost which is arbitrarily close to the non-selfish optimal. This mechanism does not incur any additional extra cost, like tolls, which are usually differentiated from the social cost as expressed in terms of delays only.

Convergence Dynamics of Resource-Homogeneous Congestion Games

Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, 2012

Many resource sharing scenarios can be modeled as congestion games. A nice property of congestion games is that simple dynamics are guaranteed to converge to Nash equilibria. Loose bounds on the convergence time are known, but exact results are difficult to obtain in general. We investigate congestion games where the resources are homogeneous but can be player-specific. In these games, players always prefer less used resources. We derive exact conditions for the longest and shortest convergence times. We also extend the results to games on graphs, where individuals only cause congestions to their neighbors. As an example, we apply our results to study cognitive radio networks, where selfish users share wireless spectrum opportunities that are constantly changing. We demonstrate how fast the users need to be able to switch channels in order to track the time-variant channel availabilities.

Maximizing social welfare in congestion games via redistribution

Games and Economic Behavior, 2015

It is well-known that efficient use of congestible resources can be achieved via marginal pricing; however, payments collected from the agents generate a budget surplus, which reduces social welfare. We show that an asymptotically first-best solution in the number of agents can be achieved by the appropriate redistribution of the budget surplus back to the agents.

A game-theoretic framework for congestion control in general topology networks

Proceedings of the 41st IEEE Conference on Decision and Control, 2002., 2002

We study control of congestion in general topology communication networks within a fairly general mathematical framework that utilizes noncooperative game theory. We consider a broad class of cost functions, composed of pricing and utility functions, which capture various pricing schemes along with varying behavior and preferences for individual users. We prove the existence and uniqueness of a Nash equilibrium under mild convexity assumptions on the cost function, and show that the Nash equilibrium is the optimal solution of a particular "system problem". Furthermore, we prove the global stability of a simple gradient algorithm and its convergence to the equilibrium point. Thus, we obtain a distributed, market-based, end-to-end framework that addresses congestion control, pricing and resource allocation problems for a large class of of communication networks. As a byproduct, we obtain a congestion control scheme for combinatorially stable ad hoc networks by specializing the cost function to a specific form. Finally, we present simulation studies that explore the effect of the cost function parameters on the equilibrium point and the robustness of the gradient algorithm to variations in time delay and to link failures.

Congestion games with malicious players

Games and Economic Behavior, 2009

We study the equilibria of non-atomic congestion games in which there are two types of players: rational players, who seek to minimize their own delay, and malicious players, who seek to maximize the average delay experienced by the rational players. We study the existence of pure and mixed Nash equilibria for these games, and we seek to quantify the impact of the malicious players on the equilibrium. One counterintuitive phenomenon which we demonstrate is the "windfall of malice": paradoxically, when a myopically malicious player gains control of a fraction of the flow, the new equilibrium may be more favorable for the remaining rational players than the previous equilibrium.