We consider the problem of routing traffic to optimize the performance of a congested network. We are given a network, a rate of traffic between each pair of nodes, and a latency function for each edge specifying the time needed to traverse the edge given its congestion; the objective is to route traffic such that the sum of all travel times—the total latency—is minimized. In many settings, it may be expensive or impossible to regulate network traffic so as to implement an optimal assignment of routes. In the absence of regulation by some central authority, we assume that each network user routes its traffic on the minimum-latency path available to it, given the network congestion caused by the other users. In general such a “selfishly motivated ” assignment of traffic to paths will not minimize the total latency; hence, this lack of regulation carries the cost of decreased network performance. In this article, we quantify the degradation in network performance due to unregulated traffic. We prove that if the latency of each edge is a linear function of its congestion, then the total latency of the routes chosen by selfish network users is at most 4/3 times the minimum possible total latency (subject to the condition that all traffic must be routed). We also consider the more general setting in which edge latency functions are assumed only to be continuous and nondecreasing in the edge congestion. Here, the total

... in networks. We consider a model of selfish routing in which the latency experienced by network tra#c on an edge of the network is a function of the edge congestion, and network users are assumed to selfishly route tra#c on minimum-latency paths. The quality of a routing of tra#c is historically measured by the sum of all travel times, also called the total latency. It is well known

We present a competitive model that describes the interaction between several competing telecommunications service providers (SPs), their subscribers, and a network owner. Competition between the service providers is assumed to take place in their pricing decisions as well as in terms of the quality of service (QoS) they offer. In turn, the subscribers' demand for the service of an SP depends not only on the price and QoS of that SP but also upon those proposed by all of its competitors. We consider two types of games to describe the competitive interactions and analyze the resulting equilibria. As quality of service measures, we consider delay, packet losses and call rejections. We establish conditions for existence and uniqueness of the equilibria, compute them explicitly and characterize their properties.

A game-theoretic model is proposed to study the cross-layer problem of joint power and rate control with quality of service (QoS) constraints in multiple-access networks. In the proposed game, each user seeks to choose its transmit power and rate in a distributed and selfish manner in order to maximize its own utility and at the same time satisfy its QoS requirements. The user’s QoS constraints are specified in terms of the average source rate and an upper bound on the average delay where the delay includes both transmission and queueing delays.. The utility function considered here measures the number of reliable bits transmitted per Joule of energy consumed and is particularly suitable for wireless networks in which energy efficiency is important. The Nash equilibrium solution for the proposed non-cooperative game is derived and a closed-form expression for the utility achieved at equilibrium is obtained. It is shown that the QoS requirements of a user translate into a “size ” for the user which is an indication of the amount of network resources consumed by the user. Using this framework, the tradeoffs among throughput, delay, network capacity and energy efficiency are also studied. In addition, we give analytical expressions for users ’ delay profiles and quantify the delay performance of the users at Nash equilibrium.

Abstract. We consider a one-round two-player network pricing game, the Stackelberg Minimum Spanning Tree game or StackMST. The game is played on a graph (representing a network), whose edges are colored either red or blue, and where the red edges have a given fixed cost (representing the competitor’s prices). The first player chooses an assignment of prices to the blue edges, and the second player then buys the cheapest possible minimum spanning tree, using any combination of red and blue edges. The goal of the first player is to maximize the total price of purchased blue edges. This game is the minimum spanning tree analog of the well-studied Stackelberg shortest-path game. We analyze the complexity and approximability of the first player’s best strategy in StackMST. In particular, we prove that the problem is APX-hard even if there are only two different red costs, and give an approximation algorithm whose approximation ratio is at most min{k, 3 + 2 ln b, 1 + ln W}, where k is the number of distinct red costs, b is the number of blue edges, and W is the maximum ratio between red costs. We also give a natural integer linear programming formulation of the problem, and show that the integrality gap of the fractional relaxation asymptotically matches the approximation guarantee of our algorithm. 1

Abstract not found

As suggested by the title of Shoham, Powers, and Grenager’s position paper [34], the ultimate lens through which the multi-agent learning framework should be assessed is “what is the question?”. In this paper, we address this question by presenting challenges motivated by engineering applications and discussing the potential appeal of multi-agent learning to meet these challenges. Moreover, we highlight various differences in the underlying assumptions and issues of concern that generally distinguish engineering applications from models that are typically considered in the economic game theory literature. 1

Most of today’s Internet routing protocols forward packets of a connection over a single path. This means that, even if redundant resources are available, a single failure (accidental or due to malicious activities) along a route will interrupt connections that use that route. Given the reactive approach to failure recovery that most current routing protocols employ, these communication disruptions may last for long enough time to be noticeable by higher protocol layers. Also, given that the path over which a connection’s packets travels is fairly predictable and easy to determine, connections are vulnerable to packet interception and eavesdropping attacks. In this paper, we introduce the Game-Theoretic Stochastic Routing (GTSR) framework, a proactive alternative to today’s reactive approaches to route repair. GTSR minimizes the impact of link and router failure by: (1) computing multiple paths between source and destination and (2) selecting among these paths randomly to forward packets. Moreover, besides improving fault-tolerance, the fact that GTSR makes packets take random paths from source to destination also improves security. For example, it makes connection eavesdropping attacks maximally difficult as the attacker would have to listen on all possible routes. The approaches developed are suitable for network layer routing as well as for application layer

A sensible design of wireless networks involves striking a good balance between an aggressive reuse of the spectral resource throughout the network and managing the resulting co-channel interference. Traditionally this problem has been tackled using a “divide and conquer” approach. The latter consists in deploying the network with a static or semi-dynamic pattern of resource reutilization. The chosen reuse factor, while sacrificing a substantial amount of efficiency, brings the interference to a tolerable level. The resource can then be managed in each cell so as to optimize the per cell capacity using an advanced air interface design. In this paper we focus our attention on the overall network capacity as a measure of system performance. We consider the problem of resource allocation and adaptive transmission in multicell scenarios. As a key instance, the problem of joint scheduling and power control simultaneously in multiple transmit-receive links, which employ capacity-achieving adaptive codes, is studied. In principle, the solution of such an optimization hinges on tough issues such as the computational complexity and the requirement for heavy receiver-to-transmitter feedback and, for cellular networks, cell-to-cell channel state information (CSI) signaling. We give asymptotic properties pertaining to rate-maximizing power control and scheduling in multicell networks. We then present some promising leads for substantial complexity and signaling reduction via the use of newly developed distributed and game theoretic techniques.

We give a brief and biased survey of the past, present, and future of research on the interface of theoretical computer science and game theory. 1